Old Molecules.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "from sympy.physics.quantum.cg import CG\n",
    "from sympy.physics.quantum import Bra, Ket, qapply, Dagger as Dag\n",
    "sp.init_printing(use_latex=True)\n",
    "import matplotlib.pyplot as plt\n",
    "import MarksConstants as mc\n",
    "import Miscellaneous as misc\n",
    "from IPython.display import display\n",
    "sp.init_printing(use_latex=True)\n",
    "from importlib import reload\n",
    "import numpy as np\n",
    "import matplotlib.style\n",
    "matplotlib.style.use('dark_background')\n",
    "import IPython.display as displayM\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lsIdentity(l,s):\n",
    "    # the identity for a single particle in the l,s basis\n",
    "    identity = sp.S(0)\n",
    "    for ml in np.arange(-l,l+1,1):\n",
    "        for ms in np.arange(-s,s+1,1):\n",
    "            identity += OKet(l,ml,s,ms)*OBra(l,ml,s,ms)\n",
    "    return identity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def jIdentity(l,s):\n",
    "    # the identity for a single particle in the l,s basis\n",
    "    identity = sp.S(0)\n",
    "    for j in np.arange(abs(l-s),l+1+1,1):\n",
    "        for mj in np.arange(-j,j+1,1):\n",
    "            identity += OKet(j,mj,l,s)*OBra(j,mj,l,s)\n",
    "    return identity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculateBOStates(l1,l2,s1,s2):\n",
    "    states = {}\n",
    "    for sigma in [0,1]:\n",
    "        for Omega in np.arange(0,l1+l2+s1+s2+1,1):\n",
    "            sigStr = 'g' if sigma==0 else 'u'\n",
    "            name = r\"$\"+str(Omega)+\"_\" +sigStr+\"$\"\n",
    "            states[name] = {}\n",
    "    LambdaLetters = ['\\Sigma', '\\Pi','\\Delta']\n",
    "    for sigma in [0,1]:\n",
    "        for L in np.arange(abs(l2-l1),l1+l2+1,1):\n",
    "            for ml in np.arange(-L,L+1,1):\n",
    "                for S in np.arange(abs(s1-s2),s1+s2+1,1):\n",
    "                    for ms in np.arange(-S,S+1,1):\n",
    "                        sigStr = 'g' if sigma==0 else 'u'\n",
    "                        name = r\"$\"+str(abs(ml+ms))+\"_\" +sigStr+\"$\"\n",
    "                        #if (ml<0 and ms<0) or (ml==0 and ms<0) or (ms==0 and ml<0):\n",
    "                        #    continue\n",
    "                        if name not in states:\n",
    "                            states[name] = {}\n",
    "                        LambdaLetter = LambdaLetters[abs(ml)]\n",
    "                        name2 = r\"$^\" + str(2*S+1) + LambdaLetter + \"_\" + sigStr + \"$\"\n",
    "                        if name2 not in states[name]:\n",
    "                            states[name][name2] = []\n",
    "                        states[name][name2].append(OKet(L,ml,S,ms,sigma))\n",
    "    return states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'OKet' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-5-dc60abb0d02f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mstates\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcalculateBOStates\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0msp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mS\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0msp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mS\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mkey\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mval\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mstates\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m     \u001b[1;31m#display(Latex(key))\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mkey2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstates\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mval\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m         \u001b[0mdisplay\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mLatex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'>>>'\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mkey2\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;34m' '\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mstates\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-4-14f746e064c6>\u001b[0m in \u001b[0;36mcalculateBOStates\u001b[1;34m(l1, l2, s1, s2)\u001b[0m\n\u001b[0;32m     22\u001b[0m                         \u001b[1;32mif\u001b[0m \u001b[0mname2\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mstates\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     23\u001b[0m                             \u001b[0mstates\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mname2\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 24\u001b[1;33m                         \u001b[0mstates\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mname2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mOKet\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mL\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mml\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mS\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mms\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0msigma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     25\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mstates\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'OKet' is not defined"
     ]
    }
   ],
   "source": [
    "states = calculateBOStates(1,1,sp.S(1)/2,sp.S(1)/2)\n",
    "for key, val in states.items():\n",
    "    #display(Latex(key))\n",
    "    for key2, states in val.items():\n",
    "        display(Latex('>>>'+key2+' '+key),states)\n",
    "    print(\"=============================================\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 995,
   "metadata": {},
   "outputs": [],
   "source": [
    "A, Delta = sp.symbols('A Delta')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 745,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = 0\n",
    "u = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 746,
   "metadata": {},
   "outputs": [],
   "source": [
    "spin1 = sp.S(1)\n",
    "proj1 = sp.S(1)\n",
    "proj0 = sp.S(0)\n",
    "spinP5 = sp.S(1)/2\n",
    "projP5 = sp.S(1)/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 747,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from stack exchange...\n",
    "class OrthogonalKet(Ket):\n",
    "    @classmethod\n",
    "    def dual_class(self):\n",
    "        return OrthogonalBra\n",
    "    def _eval_innerproduct(self, bra, **hints):\n",
    "        if len(self.args) != len(bra.args):\n",
    "            raise ValueError('Cannot multiply a ket that has a different number of labels.')\n",
    "        for i in range(len(self.args)):\n",
    "            diff = self.args[i] - bra.args[i]\n",
    "            diff.simplify()\n",
    "            if diff.is_nonzero:\n",
    "                return 0\n",
    "            if not diff.is_zero:\n",
    "                return None\n",
    "        return 1\n",
    "\n",
    "class OrthogonalBra(Bra):\n",
    "    @classmethod\n",
    "    def dual_class(self):\n",
    "        return OrthogonalKet\n",
    "OKet = OrthogonalKet\n",
    "OBra = OrthogonalBra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 748,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decomposeUpKet(ket, verbose=True):\n",
    "    return decomposeUp(*ket.args, verbose=verbose)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 749,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LStoJOperator(L,S, verbose=True):\n",
    "    # decompose the state |j1,mj1;j2,mj2> into the eigenstates of the \\vec{j}_3=\\vec{j}_1+\\vec{j}_2 operator\n",
    "    # E.g. |L,m_L; S,m_S> -> |J,m_J> \n",
    "    # Non-verbose notation: |j1,mj1;j2,mj2> = |j3,mj3,j1,2>\n",
    "    # Verbose Notation: |j1,mj1;j2,mj2> = |j3,mj3,j1,2>\n",
    "    operator = sp.S(0)\n",
    "    for j3 in np.arange(abs(L-S),L+S+1,1):\n",
    "        for mj3 in np.arange(-j3,j3+1,1):\n",
    "            for mL in np.arange(-L,L+1,1):\n",
    "                for mS in np.arange(-S,S+1,1):\n",
    "                    coef = CG(L, mL, S, mS, j3, mj3).doit()\n",
    "                    # in general most coefficients being iterated through are zero (i.e. are not part of . \n",
    "                    if coef != 0:\n",
    "                        if verbose:\n",
    "                            operator += coef * OrthogonalKet(j3, mj3, L, S)*OrthogonalBra(L, mL, S, mS)\n",
    "                        else:\n",
    "                            operator += coef * OrthogonalKet(j3, mj3)*OrthogonalBra(L, mL, S, mS)\n",
    "    return operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 750,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decomposeUp(j1,mj1,j2,mj2, verbose=False):\n",
    "    # decompose the state |j1,mj1;j2,mj2> into the eigenstates of the \\vec{j}_3=\\vec{j}_1+\\vec{j}_2 operator\n",
    "    # E.g. |L,m_L; S,m_S> -> |J,m_J> \n",
    "    # Non-verbose notation: |j1,mj1;j2,mj2> = |j3,mj3,j1,2>\n",
    "    # Verbose Notation: |j1,mj1;j2,mj2> = |j3,mj3,j1,2>\n",
    "    LHS = OrthogonalKet(j1,mj1,j2,mj2)\n",
    "    RHS = sp.S(0)\n",
    "    for j3 in np.arange(abs(j1-j2),j1+j2+1,1):\n",
    "        for mj3 in np.arange(-j3,j3+1,1):\n",
    "            coef = CG(j1, mj1, j2, mj2, j3, mj3).doit()\n",
    "            # in general most coefficients being iterated through are zero (i.e. are not part of . \n",
    "            if coef != 0:\n",
    "                if verbose:\n",
    "                    RHS += coef * OrthogonalKet(j3, mj3, j1, j2)\n",
    "                else:\n",
    "                    RHS += coef * OrthogonalKet(j3, mj3)\n",
    "    return RHS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 751,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decomposeDown(j1, mj1, j2, j3, verbose=False):\n",
    "    # Decompose |j1,mj1,j2,j3> into the eigenstates of the \\vec{j}_2 and \\vec{j}_3 operators\n",
    "    # Verbose Notation: |j1,mj1;j2;j3> = |j2,mj2;j3,mj3>\n",
    "    # Non-verbose Notation: |j1, mj1> = |j2,mj2;j3,mj3>\n",
    "    # E.g. |J,m_J> -> |L,m_L; S,m_S>\n",
    "    if verbose:\n",
    "        LHS = Ket(j1,mj1,j2,j3)\n",
    "    else:\n",
    "        LHS = Ket(j1,mj1)\n",
    "    RHS = sp.S(0)\n",
    "    for mj2 in np.arange(-j2,j2+1,1):\n",
    "        for mj3 in np.arange(-j3,j3+1,1):\n",
    "            RHS += CG(j2, mj2, j3, mj3, j1, mj1).doit() * Ket(j2,mj2,j3,mj3)\n",
    "    #display(sp.Eq(LHS,RHS))\n",
    "    return RHS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 752,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decomposeBOStateToSingle(boState):\n",
    "    # takes a two-atom BO state as input (notation |L,Lambda, S, Sigma, sigma>) where sigma = g or u\n",
    "    L, Lambda, S, ms, sigma = boState.args\n",
    "    sigma_n = 0 if sigma == g else 1\n",
    "    s = sp.S(1)/2\n",
    "    p = (-1)**(S+sigma_n)\n",
    "    oalState = 1/sp.sqrt(2)*(OKet(L,Lambda,0,0) + p * OKet(0,0,L,Lambda))\n",
    "    spinState = decomposeDown(S,ms,s,s)\n",
    "    state = oalState * spinState\n",
    "    spinSingleAtomProjection = OKet(s,s)*(OBra(s,s,s,s)+OBra(s,s,s,-s))+OKet(s,-s)*(OBra(s,-s,s,s)+OBra(s,-s,s,-s))\n",
    "    singleAtomSpin = spinSingleAtomProjection*spinState\n",
    "    singleAtomCombine = OKet(L,Lambda,s,s)*(OBra(s,s))*OBra(L,Lambda) + OKet(L,Lambda,s,-s)*(OBra(s,-s)*OBra(L,Lambda))\n",
    "    singleAtomSplit = qapply(OKet(L,Lambda)*singleAtomSpin)\n",
    "    # I think I need qapply twice because of the double ket. \n",
    "    singleAtomState = qapply(qapply(singleAtomCombine * singleAtomSplit))\n",
    "    return singleAtomState"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 873,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BoToTwoAtomStatesOperator(s1=sp.S(1)/2, s2=sp.S(1)/2):\n",
    "    operator = sp.S(0)\n",
    "    for L in [0,1]:\n",
    "        for Lambda in np.arange(-L,L+1,1):\n",
    "            for S in [0,1]:\n",
    "                for Sigma in np.arange(-S,L+1,1):\n",
    "                    for sigma in [g, u]:\n",
    "                        BoState = OKet(L,Lambda,S,Sigma,sigma)\n",
    "                        operator += decomposeBOStateToSingle(BoState,s1=s1,s2=s2) * Dag(BoState)\n",
    "    return operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 754,
   "metadata": {},
   "outputs": [],
   "source": [
    "C3, R = sp.symbols('C_3 R')\n",
    "def createBOMatrix(*states):\n",
    "    # need the BO terms, so expects form |L,Lambda,S,Sigma,sigma> although Sigma is not used.\n",
    "    matrix = sp.Matrix([[0 for _ in states] for _ in states])\n",
    "    # the matrix is diagonal.\n",
    "    for num, state in enumerate(states):\n",
    "        L, Lambda, S, Sigma, sigma = state.args\n",
    "        p = (-1)**(S+sigma)\n",
    "        matrix[num,num] = -p*(3*Lambda**2-L*(L+1))/R**3 * C3\n",
    "    return matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 756,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createMovrePichlerMatrix(*states):\n",
    "    num = len(states)\n",
    "    matrix = sp.Matrix([[0 for _ in states] for _ in states])\n",
    "    for num, _ in enumerate(states):\n",
    "        matrix[num,num] = (-A/2).subs(A,2*Delta/3)\n",
    "    for num1, state1 in enumerate(states):\n",
    "        for num2, state2 in enumerate(states):\n",
    "            Jstate1 = qapply(L1Sp5ToJ*BOto2*state1)\n",
    "            Jstate2 = qapply(L1Sp5ToJ*BOto2*state2)\n",
    "            matrix[num1,num2] += qapply(Dag(Jstate1)*fs*Jstate2).subs(A,2*Delta/3)\n",
    "    return matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Alkali"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 777,
   "metadata": {},
   "outputs": [],
   "source": [
    "BOto2 = BoToTwoAtomStatesOperator()\n",
    "fs = fineStructureInteraction(spin1,spinP5)\n",
    "L1Sp5ToJ = LStoJOperator(spin1, spinP5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 888,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0^-_g$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{2 \\Delta}{3} & \\frac{\\sqrt{2} \\Delta}{3} & 0 & 0\\\\\\frac{\\sqrt{2} \\Delta}{3} & - \\frac{\\Delta}{3} & 0 & 0\\\\0 & 0 & - \\frac{2 \\Delta}{3} & \\frac{\\sqrt{2} \\Delta}{3}\\\\0 & 0 & \\frac{\\sqrt{2} \\Delta}{3} & - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-2⋅Δ   √2⋅Δ             ⎤\n",
       "⎢─────  ────    0     0  ⎥\n",
       "⎢  3     3               ⎥\n",
       "⎢                        ⎥\n",
       "⎢√2⋅Δ   -Δ               ⎥\n",
       "⎢────   ───     0     0  ⎥\n",
       "⎢ 3      3               ⎥\n",
       "⎢                        ⎥\n",
       "⎢             -2⋅Δ   √2⋅Δ⎥\n",
       "⎢  0     0    ─────  ────⎥\n",
       "⎢               3     3  ⎥\n",
       "⎢                        ⎥\n",
       "⎢             √2⋅Δ   -Δ  ⎥\n",
       "⎢  0     0    ────   ─── ⎥\n",
       "⎣              3      3  ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State0mg_3Sigmg = OKet(1,0,1,0,g)\n",
    "State3Pig1 = OKet(1,1,1,-1,g)\n",
    "State3Pig2 = OKet(1,-1,1,1,g)\n",
    "State0mg_3Pig = 1/sp.sqrt(2)*(State3Pig1+State3Pig2)\n",
    "State0pg_3Pig = 1/sp.sqrt(2)*(State3Pig1-State3Pig2)\n",
    "State0pg_3Sigmg = OKet(1,0,0,0,g)\n",
    "V_0_m_g = createMovrePichlerMatrix(State0mg_3Pig,State0mg_3Sigmg,State0pg_3Pig,State0pg_3Sigmg)\n",
    "display(Latex('$0^-_g$:'), V_0_m_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 781,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0^-_g$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{C_{3}}{R^{3}} - \\frac{2 \\Delta}{3} & \\frac{\\sqrt{2} \\Delta}{3}\\\\\\frac{\\sqrt{2} \\Delta}{3} & - \\frac{2 C_{3}}{R^{3}} - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C₃   2⋅Δ     √2⋅Δ   ⎤\n",
       "⎢── - ───     ────   ⎥\n",
       "⎢ 3    3       3     ⎥\n",
       "⎢R                   ⎥\n",
       "⎢                    ⎥\n",
       "⎢  √2⋅Δ      2⋅C₃   Δ⎥\n",
       "⎢  ────    - ──── - ─⎥\n",
       "⎢   3          3    3⎥\n",
       "⎣             R      ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$0^+_g$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{C_{3}}{R^{3}} - \\frac{2 \\Delta}{3} & \\frac{\\sqrt{2} \\Delta}{3}\\\\\\frac{\\sqrt{2} \\Delta}{3} & \\frac{2 C_{3}}{R^{3}} - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C₃   2⋅Δ    √2⋅Δ  ⎤\n",
       "⎢── - ───    ────  ⎥\n",
       "⎢ 3    3      3    ⎥\n",
       "⎢R                 ⎥\n",
       "⎢                  ⎥\n",
       "⎢  √2⋅Δ    2⋅C₃   Δ⎥\n",
       "⎢  ────    ──── - ─⎥\n",
       "⎢   3        3    3⎥\n",
       "⎣           R      ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$0^-_u$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{C_{3}}{R^{3}} - \\frac{2 \\Delta}{3} & \\frac{\\sqrt{2} \\Delta}{3}\\\\\\frac{\\sqrt{2} \\Delta}{3} & - \\frac{2 C_{3}}{R^{3}} - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  C₃   2⋅Δ     √2⋅Δ   ⎤\n",
       "⎢- ── - ───     ────   ⎥\n",
       "⎢   3    3       3     ⎥\n",
       "⎢  R                   ⎥\n",
       "⎢                      ⎥\n",
       "⎢   √2⋅Δ       2⋅C₃   Δ⎥\n",
       "⎢   ────     - ──── - ─⎥\n",
       "⎢    3           3    3⎥\n",
       "⎣               R      ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$0^+_u$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{C_{3}}{R^{3}} - \\frac{2 \\Delta}{3} & \\frac{\\sqrt{2} \\Delta}{3}\\\\\\frac{\\sqrt{2} \\Delta}{3} & \\frac{2 C_{3}}{R^{3}} - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  C₃   2⋅Δ    √2⋅Δ  ⎤\n",
       "⎢- ── - ───    ────  ⎥\n",
       "⎢   3    3      3    ⎥\n",
       "⎢  R                 ⎥\n",
       "⎢                    ⎥\n",
       "⎢   √2⋅Δ     2⋅C₃   Δ⎥\n",
       "⎢   ────     ──── - ─⎥\n",
       "⎢    3         3    3⎥\n",
       "⎣             R      ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$1_g$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3} & \\frac{\\Delta}{3} & \\frac{\\Delta}{3}\\\\\\frac{\\Delta}{3} & - \\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3} & - \\frac{\\Delta}{3}\\\\\\frac{\\Delta}{3} & - \\frac{\\Delta}{3} & - \\frac{2 C_{3}}{R^{3}} - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C₃   Δ     Δ          Δ     ⎤\n",
       "⎢── - ─     ─          ─     ⎥\n",
       "⎢ 3   3     3          3     ⎥\n",
       "⎢R                           ⎥\n",
       "⎢                            ⎥\n",
       "⎢  Δ       C₃   Δ     -Δ     ⎥\n",
       "⎢  ─     - ── - ─     ───    ⎥\n",
       "⎢  3        3   3      3     ⎥\n",
       "⎢          R                 ⎥\n",
       "⎢                            ⎥\n",
       "⎢  Δ       -Δ        2⋅C₃   Δ⎥\n",
       "⎢  ─       ───     - ──── - ─⎥\n",
       "⎢  3        3          3    3⎥\n",
       "⎣                     R      ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$1_g$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3} & \\frac{\\Delta}{3} & \\frac{\\Delta}{3}\\\\\\frac{\\Delta}{3} & \\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3} & - \\frac{\\Delta}{3}\\\\\\frac{\\Delta}{3} & - \\frac{\\Delta}{3} & \\frac{2 C_{3}}{R^{3}} - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  C₃   Δ    Δ        Δ    ⎤\n",
       "⎢- ── - ─    ─        ─    ⎥\n",
       "⎢   3   3    3        3    ⎥\n",
       "⎢  R                       ⎥\n",
       "⎢                          ⎥\n",
       "⎢   Δ      C₃   Δ    -Δ    ⎥\n",
       "⎢   ─      ── - ─    ───   ⎥\n",
       "⎢   3       3   3     3    ⎥\n",
       "⎢          R               ⎥\n",
       "⎢                          ⎥\n",
       "⎢   Δ       -Δ     2⋅C₃   Δ⎥\n",
       "⎢   ─       ───    ──── - ─⎥\n",
       "⎢   3        3       3    3⎥\n",
       "⎣                   R      ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State0mg_3Sigmg = OKet(1,0,1,0,g)\n",
    "State3Pig1 = OKet(1,1,1,-1,g)\n",
    "State3Pig2 = OKet(1,-1,1,1,g)\n",
    "State0mg_3Pig = 1/sp.sqrt(2)*(State3Pig1+State3Pig2)\n",
    "V_0_m_g = createBOMatrix(State3Pig1, State0mg_3Sigmg)+createMovrePichlerMatrix(State0mg_3Pig,State0mg_3Sigmg)\n",
    "display(Latex('$0^-_g$:'), V_0_m_g)\n",
    "\n",
    "State0pg_1Sigpg = OKet(1,0,0,0,g)\n",
    "State0pg_3Pig = 1/sp.sqrt(2)*(State3Pig1-State3Pig2)\n",
    "V_0_p_g = createBOMatrix(State3Pig1, State0pg_1Sigpg)+createMovrePichlerMatrix(State0pg_3Pig, State0pg_1Sigpg)\n",
    "display(Latex('$0^+_g$:'), V_0_p_g)\n",
    "\n",
    "State3Piu1 = OKet(1,1,1,-1,u)\n",
    "State3Piu2 = OKet(1,-1,1,1,u)\n",
    "State0mu_3Piu = 1/sp.sqrt(2) * (State3Piu1-State3Piu2)\n",
    "State0mu_1Sigmu = OKet(1,0,0,0,u)\n",
    "V_0_m_u = createBOMatrix(State3Piu1, State0mu_1Sigmu)+createMovrePichlerMatrix(State0mu_3Piu,State0mu_1Sigmu)\n",
    "display(Latex('$0^-_u$:'),V_0_m_u)\n",
    "\n",
    "State0pu_3Piu = 1/sp.sqrt(2) * (State3Piu1+State3Piu2)\n",
    "State0pu_3Sigpu = OKet(1,0,1,0,u)\n",
    "V_0_p_u = createBOMatrix(State3Piu1, State0pu_3Sigpu)+createMovrePichlerMatrix(State0pu_3Piu,State0pu_3Sigpu)\n",
    "display(Latex('$0^+_u$:'),V_0_p_u)\n",
    "\n",
    "State1g_3Pig = OKet(1,1,1,0,g)\n",
    "State1g_1Pig = OKet(1,1,0,0,g)\n",
    "State1g_3Sigpg = OKet(1,0,1,1,g)\n",
    "V_1_g = createBOMatrix(State1g_3Pig, State1g_1Pig, State1g_3Sigpg )+createMovrePichlerMatrix( State1g_3Pig, State1g_1Pig, State1g_3Sigpg)\n",
    "display(Latex('$1_g$:'),V_1_g)\n",
    "\n",
    "State1u_3Piu = OKet(1,1,1,0,u)\n",
    "State1u_1Piu = OKet(1,1,0,0,u)\n",
    "State1u_3Sigmu = OKet(1,0,1,1,u)\n",
    "V_1_u = createBOMatrix(State1u_3Piu, State1u_1Piu, State1u_3Sigmu )+createMovrePichlerMatrix( State1u_3Piu, State1u_1Piu, State1u_3Sigmu)\n",
    "display(Latex('$1_g$:'),V_1_u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 767,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.7197635548748796e-21 5.94492796981645e-48\n"
     ]
    }
   ],
   "source": [
    "lifetime = (mc.Rb87_D1_Lifetime+mc.Rb87_D2_Lifetime)/2\n",
    "transFreq = 2*np.pi*(mc.Rb87_D2LineFrequency+mc.Rb87_D1LineFrequency)/2\n",
    "DeltaVal = mc.h*(mc.Rb87_D2LineFrequency-mc.Rb87_D1LineFrequency)# / mc.h\n",
    "C_3_val = 3*mc.hbar*mc.c**3/(4*lifetime*transFreq**3)# * 1e27 / mc.h\n",
    "C_3_val = mc.Rb87_C3\n",
    "print(DeltaVal, C_3_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1061,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ - \\frac{3 C_{3} + 2 \\Delta R^{3}}{3 R^{3}} : 1, \\  \\frac{3 C_{3} - 2 \\Delta R^{3} - 3 \\sqrt{9 C_{3}^{2} + 4 C_{3} \\Delta R^{3} + 4 \\Delta^{2} R^{6}}}{6 R^{3}} : 1, \\  \\frac{3 C_{3} - 2 \\Delta R^{3} + 3 \\sqrt{9 C_{3}^{2} + 4 C_{3} \\Delta R^{3} + 4 \\Delta^{2} R^{6}}}{6 R^{3}} : 1\\right\\}$"
      ],
      "text/plain": [
       "⎧                                           _____________________________     \n",
       "⎪ ⎛            3⎞                  3       ╱     2           3      2  6      \n",
       "⎪-⎝3⋅C₃ + 2⋅Δ⋅R ⎠      3⋅C₃ - 2⋅Δ⋅R  - 3⋅╲╱  9⋅C₃  + 4⋅C₃⋅Δ⋅R  + 4⋅Δ ⋅R       \n",
       "⎨─────────────────: 1, ──────────────────────────────────────────────────: 1, \n",
       "⎪          3                                     3                            \n",
       "⎪       3⋅R                                   6⋅R                             \n",
       "⎩                                                                             \n",
       "\n",
       "                     _____________________________   ⎫\n",
       "            3       ╱     2           3      2  6    ⎪\n",
       "3⋅C₃ - 2⋅Δ⋅R  + 3⋅╲╱  9⋅C₃  + 4⋅C₃⋅Δ⋅R  + 4⋅Δ ⋅R     ⎪\n",
       "──────────────────────────────────────────────────: 1⎬\n",
       "                          3                          ⎪\n",
       "                       6⋅R                           ⎪\n",
       "                                                     ⎭"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rOQS4DbgcjQDcA3yaoQsFfWzO7M2oC63qptmw4UNRmglmc93KS6S8Gti1SOpZ1EjdsIwStcBcZPy3Rfb1ABuhcAjrAeORa8LJwEORdJsBvwDGBumuQq9yNYworwc+BZyHRqImA99BflMXBGl8bM7szagLreqm2bDhQ1GaCWZz3choNOr+QtLBUX19fa4vfx/5NO1UdKlyMgc4Bvl+rYjsX4ReGzoH2ASFSHgY+EzVBTQ6grXAXShURshs9KaacCrKbM5oCqabRtmYZhojYSVwLXBi0sGsVfwXADsih/t28U3k3zKNoSILcry+Ndj/J+AE4JPArlUW0OgYHgfui+27H9gm8tlszmgCpptGFZhmGq2yF/A6FAEikawG6jLgXOR0/5qMtGVwPhoB2B8ZfZTt0MrU5ZF9K9F01tGVlM7oNJYwfLbgDciuwGzOaAamm0ZVmGYarTAW+DbwU4a6Hw3BJw7qKcCvgDuB05DPQBXMQzG5jkQO/hODbaPgeA9yrn0g9r3rgcOqKaLRYZwHvAXZ+Q7AB4CTGOpLZTZn1BnTTaNKTDONvGwH/BJYAxzvSujTQH0JNVLfGvxf1dsdTkQrUG9A0wjhFr6ZoAf5tcSda69HPTqbPjDycgdalfpBFKbnbOAr6KEPZnNG/THdNKrENNPIw6vRC04WAO8kJbxUSNYiKcMwDMMwDMOolDq/6tQwDMMwDMPoQqyBahiGYRiGYdQKa6AahmEYhmEYteL/E1Dqhzbylu0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ \\frac{3 C_{3} - \\Delta R^{3}}{2 R^{3}} - \\frac{\\sqrt{3} \\sqrt{3 C_{3}^{2} + 2 C_{3} \\Delta R^{3} + 3 \\Delta^{2} R^{6}}}{6 R^{3}} : 1, \\  \\frac{3 C_{3} - \\Delta R^{3}}{2 R^{3}} + \\frac{\\sqrt{3} \\sqrt{3 C_{3}^{2} + 2 C_{3} \\Delta R^{3} + 3 \\Delta^{2} R^{6}}}{6 R^{3}} : 1\\right\\}$"
      ],
      "text/plain": [
       "⎧                    _____________________________                         ___\n",
       "⎪          3        ╱     2           3      2  6                3        ╱   \n",
       "⎪3⋅C₃ - Δ⋅R    √3⋅╲╱  3⋅C₃  + 2⋅C₃⋅Δ⋅R  + 3⋅Δ ⋅R       3⋅C₃ - Δ⋅R    √3⋅╲╱  3⋅\n",
       "⎨─────────── - ───────────────────────────────────: 1, ─────────── + ─────────\n",
       "⎪       3                         3                           3               \n",
       "⎪    2⋅R                       6⋅R                         2⋅R                \n",
       "⎩                                                                             \n",
       "\n",
       "__________________________   ⎫\n",
       "  2           3      2  6    ⎪\n",
       "C₃  + 2⋅C₃⋅Δ⋅R  + 3⋅Δ ⋅R     ⎪\n",
       "──────────────────────────: 1⎬\n",
       "          3                  ⎪\n",
       "       6⋅R                   ⎪\n",
       "                             ⎭"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ - \\frac{3 C_{3} + \\Delta R^{3}}{2 R^{3}} - \\frac{\\sqrt{3} \\sqrt{3 C_{3}^{2} - 2 C_{3} \\Delta R^{3} + 3 \\Delta^{2} R^{6}}}{6 R^{3}} : 1, \\  - \\frac{3 C_{3} + \\Delta R^{3}}{2 R^{3}} + \\frac{\\sqrt{3} \\sqrt{3 C_{3}^{2} - 2 C_{3} \\Delta R^{3} + 3 \\Delta^{2} R^{6}}}{6 R^{3}} : 1\\right\\}$"
      ],
      "text/plain": [
       "⎧                      _____________________________                          \n",
       "⎪            3        ╱     2           3      2  6                  3        \n",
       "⎪  3⋅C₃ + Δ⋅R    √3⋅╲╱  3⋅C₃  - 2⋅C₃⋅Δ⋅R  + 3⋅Δ ⋅R         3⋅C₃ + Δ⋅R    √3⋅╲╱\n",
       "⎨- ─────────── - ───────────────────────────────────: 1, - ─────────── + ─────\n",
       "⎪         3                         3                             3           \n",
       "⎪      2⋅R                       6⋅R                           2⋅R            \n",
       "⎩                                                                             \n",
       "\n",
       " _____________________________   ⎫\n",
       "╱     2           3      2  6    ⎪\n",
       "  3⋅C₃  - 2⋅C₃⋅Δ⋅R  + 3⋅Δ ⋅R     ⎪\n",
       "──────────────────────────────: 1⎬\n",
       "              3                  ⎪\n",
       "           6⋅R                   ⎪\n",
       "                                 ⎭"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0L0VZ2scwDMMwDKNhsQKXYRiGYRhGxliByzAMwzAMI2P+D2JQu5N3kLQSAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ \\frac{C_{3} - \\Delta R^{3}}{2 R^{3}} - \\frac{\\sqrt{9 C_{3}^{2} + 2 C_{3} \\Delta R^{3} + \\Delta^{2} R^{6}}}{2 R^{3}} : 1, \\  \\frac{C_{3} - \\Delta R^{3}}{2 R^{3}} + \\frac{\\sqrt{9 C_{3}^{2} + 2 C_{3} \\Delta R^{3} + \\Delta^{2} R^{6}}}{2 R^{3}} : 1\\right\\}$"
      ],
      "text/plain": [
       "⎧               ___________________________                    _______________\n",
       "⎪        3     ╱     2           3    2  6              3     ╱     2         \n",
       "⎪C₃ - Δ⋅R    ╲╱  9⋅C₃  + 2⋅C₃⋅Δ⋅R  + Δ ⋅R       C₃ - Δ⋅R    ╲╱  9⋅C₃  + 2⋅C₃⋅Δ\n",
       "⎨───────── - ──────────────────────────────: 1, ───────── + ──────────────────\n",
       "⎪      3                     3                        3                     3 \n",
       "⎪   2⋅R                   2⋅R                      2⋅R                   2⋅R  \n",
       "⎩                                                                             \n",
       "\n",
       "____________   ⎫\n",
       "  3    2  6    ⎪\n",
       "⋅R  + Δ ⋅R     ⎪\n",
       "────────────: 1⎬\n",
       "               ⎪\n",
       "               ⎪\n",
       "               ⎭"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2,2,figsize=(20,10))\n",
    "Rvals = np.linspace( 20*mc.a0, 2000*mc.a0, 3000 )\n",
    "potentialList = [V_0_m_g, V_0_p_g, V_0_m_u, V_0_p_u, V_1_g, V_1_u]\n",
    "names=[r'$0^-_g$',r'$0^+_g$',r'$0^-_u$',r'$0^+_u$',r'$1_g$',r'$1_u$', r'$2_g$', r'$2_u$']\n",
    "linestyles=[':','-','-.',':','-','-.',':','-','-.',':','-','-.']\n",
    "colors, _ = misc.getColors(len(potentialList)+3, cmStr='viridis')\n",
    "\n",
    "data = [[] for _ in range(len(potentialList)+2)]\n",
    "\n",
    "for matrixnum, (name, potentialMatrix, c_) in enumerate(zip(names, potentialList, colors)):\n",
    "    if matrixnum < 4:\n",
    "        display(potentialMatrix.eigenvals())\n",
    "    matrixFunc = sp.lambdify(R, potentialMatrix.subs(C3,C_3_val).subs(Delta,DeltaVal), 'numpy')\n",
    "    for rv in Rvals:\n",
    "        data[matrixnum].append(sorted(np.linalg.eigvals(matrixFunc(rv))))\n",
    "data[-2] = np.array([C_3_val/rv**3 for rv in Rvals])\n",
    "data[-1] = np.array([-C_3_val/rv**3 for rv in Rvals])\n",
    "for ax in axs.flatten():\n",
    "    ax.axhline(-0.0729113, alpha=0.2,color='r')\n",
    "    ax.axhline(-0.2298518, alpha=0.2,color='r')\n",
    "    ax.axhline(-0.30207388, alpha=0.2,color='r')\n",
    "    ax.axhline(-DeltaVal* 1e-9 / mc.h+0.306246, alpha=0.2,color='r')\n",
    "    ax.axhline(-DeltaVal* 1e-9 / mc.h-0.510410, alpha=0.2,color='r')\n",
    "    for name, mdata, c_, linestyle in zip(names, data, colors, linestyles):\n",
    "        if len(np.array(mdata).shape) == 2 or len(np.array(mdata).shape) == 3:\n",
    "            for lineNum, lineData in enumerate(misc.transpose(mdata)):\n",
    "                ax.plot(Rvals*1e9, np.array(lineData) * 1e-9 / mc.h, label=name if lineNum == 0 else None, color=c_, linestyle=linestyle)\n",
    "        else:\n",
    "            ax.plot(Rvals*1e9, np.array(mdata) * 1e-9 / mc.h, label=name, color=c_, linestyle=linestyle)\n",
    "    ax.set_xlabel('Inter-nuclear distance (nm)')\n",
    "    ax.set_ylabel('Energy (GHz)')\n",
    "    ax.grid(alpha=0.1)\n",
    "    ax.axhline(0.1937408, alpha=0.2,color='r', label='F States')\n",
    "\n",
    "axs[0,0].set_title('Full Range')\n",
    "axs[0,0].set_xlim(min(Rvals)*1e9,max(Rvals)*1e9/20)\n",
    "axs[0,0].legend(ncol=5,fontsize=14)\n",
    "axs[1,0].set_title('Zoom $5P_{3/2}$')\n",
    "axs[1,0].set_xlim(min(Rvals)*1e9,max(Rvals)*1e9/10)\n",
    "axs[1,0].set_ylim(-1000, 500)\n",
    "axs[0,1].set_title('Super-Zoom $5P_{3/2}$')\n",
    "axs[0,1].set_xlim(min(Rvals)*1e9,max(Rvals)*1e9)\n",
    "axs[0,1].set_ylim(-0.35, 0.25)\n",
    "axs[1,1].set_title('Zoom $5P_{1/2}$')\n",
    "axs[1,1].set_xlim(min(Rvals)*1e9,max(Rvals)*1e9/10)\n",
    "axs[1,1].set_ylim(-8000, -6000);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Alkali Earth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 876,
   "metadata": {},
   "outputs": [],
   "source": [
    "BOto2 = BoToTwoAtomStatesOperator()\n",
    "fs_1_p5 = fineStructureInteraction(spin1,spinP5)\n",
    "L1Sp5ToJ = LStoJOperator(spin1, spinP5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 867,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decomposeBOStateToSingle(boState, s1 = sp.S(1)/2, s2 = sp.S(1)/2):\n",
    "    # takes a two-atom BO state as input (notation |L,Lambda, S, Sigma, sigma>) where sigma = g or u\n",
    "    L, Lambda, S, ms, sigma = boState.args\n",
    "    sigma_n = 0 if sigma == g else 1\n",
    "    p = (-1)**(S+sigma_n)\n",
    "    oalState = 1/sp.sqrt(2)*(OKet(L,Lambda,0,0) + p * OKet(0,0,L,Lambda))\n",
    "    spinState = decomposeDown(S,ms,s1,s2)\n",
    "    state = oalState * spinState\n",
    "    # trace out the second atom\n",
    "    spinSingleAtomProjection = sp.S(0)\n",
    "    for ms1 in np.arange(-s1, s1+1,1):\n",
    "        brasTerm = sp.S(0)\n",
    "        for ms2 in np.arange(-s2,s2+1,1):\n",
    "            brasTerm += OBra(s1,ms1,s2,ms2)\n",
    "        # use the 's' in order to distinguish between the spin part and the oal part. \n",
    "        # Without this there seem to be occasional problems within sympy in evaluating inner products\n",
    "        spinSingleAtomProjection += qapply(OKet('s',s1, ms1)*brasTerm)\n",
    "    singleAtomSpin = qapply(spinSingleAtomProjection*spinState)\n",
    "\n",
    "    # just combine the two kets for the oal portion and spin portion into one ket\n",
    "    singleAtomCombine = sp.S(0)\n",
    "    for ms1 in np.arange(-s1, s1+1,1): \n",
    "        singleAtomCombine += OKet(L,Lambda, s1, ms1) * OBra('s',s1,ms1) * OBra(L,Lambda)\n",
    "    singleAtomSplit = qapply(OKet(L,Lambda)*singleAtomSpin)\n",
    "    # I think I need qapply twice because of the double ket.\n",
    "    singleAtomState = qapply(qapply(singleAtomCombine * singleAtomSplit)).doit()\n",
    "    return singleAtomState"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 941,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createMovrePichlerMatrix(*states,fineStructureOperator=fs,BOto2AtomOperator=BOto2,LStoJOperator=L1Sp5ToJ, offset=-A/2, \n",
    "                             subs={A:2*Delta/3}):\n",
    "    num = len(states)\n",
    "    matrix = sp.Matrix([[0 for _ in states] for _ in states])\n",
    "    for num, _ in enumerate(states):\n",
    "        matrix[num,num] = offset.subs(subs)\n",
    "    for num1, state1 in enumerate(states):\n",
    "        for num2, state2 in enumerate(states):\n",
    "            Jstate1 = qapply(LStoJOperator*BOto2AtomOperator*state1)\n",
    "            Jstate2 = qapply(LStoJOperator*BOto2AtomOperator*state2)\n",
    "            matrix[num1,num2] += qapply(Dag(Jstate1)*fineStructureOperator*Jstate2).subs(subs)\n",
    "    return matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 877,
   "metadata": {},
   "outputs": [],
   "source": [
    "L1S1ToJ = LStoJOperator(spin1, spin1)\n",
    "fs_1_1 = fineStructureInteraction(spin1, spin1)\n",
    "BOto2_s1e1_s2e0 = BoToTwoAtomStatesOperator(s1=sp.S(1), s2=sp.S(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 963,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0^\\pm_g$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3} & \\frac{\\sqrt{2} \\Delta}{3} & 0\\\\\\frac{\\sqrt{2} \\Delta}{3} & - \\frac{2 C_{3}}{R^{3}} & 0\\\\0 & 0 & \\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C₃   Δ   √2⋅Δ         ⎤\n",
       "⎢── - ─   ────     0   ⎥\n",
       "⎢ 3   3    3           ⎥\n",
       "⎢R                     ⎥\n",
       "⎢                      ⎥\n",
       "⎢ √2⋅Δ   -2⋅C₃         ⎥\n",
       "⎢ ────   ──────    0   ⎥\n",
       "⎢  3        3          ⎥\n",
       "⎢          R           ⎥\n",
       "⎢                      ⎥\n",
       "⎢                C₃   Δ⎥\n",
       "⎢  0       0     ── - ─⎥\n",
       "⎢                 3   3⎥\n",
       "⎣                R     ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State0mg_3Sigmg = OKet(1,0,1,0,g)\n",
    "State3Pig1 = OKet(1,1,1,-1,g)\n",
    "State3Pig2 = OKet(1,-1,1,1,g)\n",
    "State0mg_3Pig = 1/sp.sqrt(2)*(State3Pig1+State3Pig2)\n",
    "State0pg_3Pig = 1/sp.sqrt(2)*(State3Pig1-State3Pig2)\n",
    "\n",
    "V_0_pm_g = (createBOMatrix(State3Pig1, State0mg_3Sigmg, State3Pig1) \n",
    "            + createMovrePichlerMatrix( State0mg_3Pig, State0mg_3Sigmg, State0pg_3Pig, fineStructureOperator=fs_1_1, offset=sp.S(0), \n",
    "                                        BOto2AtomOperator=BOto2_s1e1_s2e0, LStoJOperator=L1S1ToJ, subs={A:Delta/3} ))\n",
    "display(Latex('$0^\\pm_g$:'), V_0_pm_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 964,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0^\\pm_u$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3} & \\frac{\\sqrt{2} \\Delta}{3} & 0\\\\\\frac{\\sqrt{2} \\Delta}{3} & \\frac{2 C_{3}}{R^{3}} & 0\\\\0 & 0 & - \\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  C₃   Δ  √2⋅Δ          ⎤\n",
       "⎢- ── - ─  ────     0    ⎥\n",
       "⎢   3   3   3            ⎥\n",
       "⎢  R                     ⎥\n",
       "⎢                        ⎥\n",
       "⎢  √2⋅Δ    2⋅C₃          ⎥\n",
       "⎢  ────    ────     0    ⎥\n",
       "⎢   3        3           ⎥\n",
       "⎢           R            ⎥\n",
       "⎢                        ⎥\n",
       "⎢                  C₃   Δ⎥\n",
       "⎢   0       0    - ── - ─⎥\n",
       "⎢                   3   3⎥\n",
       "⎣                  R     ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State0mu_3Sigmu = OKet(1,0,1,0,u)\n",
    "State3Piu1 = OKet(1,1,1,-1,u)\n",
    "State3Piu2 = OKet(1,-1,1,1,u)\n",
    "State0mu_3Piu = 1/sp.sqrt(2)*(State3Pig1+State3Pig2)\n",
    "State0pu_3Piu = 1/sp.sqrt(2)*(State3Pig1-State3Pig2)\n",
    "\n",
    "V_0_pm_u = (createBOMatrix(State3Piu1, State0mu_3Sigmu, State3Piu1) \n",
    "            + createMovrePichlerMatrix( State0mu_3Piu, State0mu_3Sigmu, State0pu_3Piu, fineStructureOperator=fs_1_1, offset=sp.S(0), \n",
    "                                        BOto2AtomOperator=BOto2_s1e1_s2e0, LStoJOperator=L1S1ToJ, subs={A:Delta/3} ))\n",
    "\n",
    "display(Latex('$0^\\pm_u$:'), V_0_pm_u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 965,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1_g$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{C_{3}}{R^{3}} & \\frac{\\Delta}{3}\\\\\\frac{\\Delta}{3} & - \\frac{2 C_{3}}{R^{3}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C₃    Δ   ⎤\n",
       "⎢──    ─   ⎥\n",
       "⎢ 3    3   ⎥\n",
       "⎢R         ⎥\n",
       "⎢          ⎥\n",
       "⎢Δ   -2⋅C₃ ⎥\n",
       "⎢─   ──────⎥\n",
       "⎢3      3  ⎥\n",
       "⎣      R   ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State1g_3Pig_p = OKet(1,1,1,0,g)\n",
    "State1g_3Pig_m = OKet(1,-1,1,0,g)\n",
    "State1g_3Sigmag_p = OKet(1,0,1,1,g)\n",
    "State1g_3Sigmag_m = OKet(1,0,1,-1,g)\n",
    "V_1_g = (createBOMatrix(*(State1g_3Pig_p, State1g_3Sigmag_p))\n",
    "                         + createMovrePichlerMatrix(*(State1g_3Pig_p, State1g_3Sigmag_p), fineStructureOperator=fs_1_1, offset=sp.S(0), \n",
    "                                                     BOto2AtomOperator=BOto2_s1e1_s2e0, LStoJOperator=L1S1ToJ, subs={A:Delta/3}))\n",
    "display(Latex('$1_g$:'), V_1_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 966,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1_u$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{C_{3}}{R^{3}} & \\frac{\\Delta}{3}\\\\\\frac{\\Delta}{3} & \\frac{2 C_{3}}{R^{3}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-C₃    Δ  ⎤\n",
       "⎢────   ─  ⎥\n",
       "⎢  3    3  ⎥\n",
       "⎢ R        ⎥\n",
       "⎢          ⎥\n",
       "⎢ Δ    2⋅C₃⎥\n",
       "⎢ ─    ────⎥\n",
       "⎢ 3      3 ⎥\n",
       "⎣       R  ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State1g_3Pig_p = OKet(1,1,1,0,u)\n",
    "State1g_3Pig_m = OKet(1,-1,1,0,u)\n",
    "State1g_3Sigmag_p = OKet(1,0,1,1,u)\n",
    "State1g_3Sigmag_m = OKet(1,0,1,-1,u)\n",
    "V_1_u = (createBOMatrix(*(State1g_3Pig_p, State1g_3Sigmag_p))\n",
    "                         + createMovrePichlerMatrix(*(State1g_3Pig_p, State1g_3Sigmag_p), fineStructureOperator=fs_1_1, offset=sp.S(0), \n",
    "                                                     BOto2AtomOperator=BOto2_s1e1_s2e0, LStoJOperator=L1S1ToJ, subs={A:Delta/3}))\n",
    "display(Latex('$1_u$:'), V_1_u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 967,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2_g$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{C_{3}}{R^{3}} + \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C₃   Δ⎤\n",
       "⎢── + ─⎥\n",
       "⎢ 3   3⎥\n",
       "⎣R     ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State2g_3Pig = OKet(1,1,1,1,g)\n",
    "State2g_3Piu = OKet(1,1,1,1,u)\n",
    "V_2_g = (createBOMatrix(State2g_3Pig)\n",
    "                         + createMovrePichlerMatrix(State2g_3Pig, fineStructureOperator=fs_1_1, offset=sp.S(0), \n",
    "                                                     BOto2AtomOperator=BOto2_s1e1_s2e0, LStoJOperator=L1S1ToJ, subs={A:Delta/3}))\n",
    "display(Latex('$2_g$:'), V_2_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 968,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2_u$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{C_{3}}{R^{3}} + \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  C₃   Δ⎤\n",
       "⎢- ── + ─⎥\n",
       "⎢   3   3⎥\n",
       "⎣  R     ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State2g_3Piu = OKet(1,1,1,1,u)\n",
    "V_2_u = (createBOMatrix(State2g_3Piu)\n",
    "                         + createMovrePichlerMatrix(State2g_3Piu, fineStructureOperator=fs_1_1, offset=sp.S(0), \n",
    "                                                     BOto2AtomOperator=BOto2_s1e1_s2e0, LStoJOperator=L1S1ToJ, subs={A:Delta/3}))\n",
    "display(Latex('$2_u$:'), V_2_u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "LStoJOperator*BOto2AtomOperator*state1\n",
    "State2g_3Pig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "DeltaVal/mc.h*1e-9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 978,
   "metadata": {},
   "outputs": [],
   "source": [
    "SrDeltaVal = mc.h*mc.c/(671e-9)-mc.h*mc.c/ (698e-9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 987,
   "metadata": {},
   "outputs": [],
   "source": [
    "lifetime = 21.4e-6\n",
    "transFreq = mc.c/(689e-9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 990,
   "metadata": {},
   "outputs": [],
   "source": [
    "Sr_C_3_Val = 3*mc.hbar*mc.c**3/(4*lifetime*transFreq**3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1060,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ \\frac{3 C_{3} - \\Delta R^{3}}{3 R^{3}} : 1, \\  - \\frac{3 C_{3} + \\Delta R^{3} - 3 \\sqrt{9 C_{3}^{2} - 2 C_{3} \\Delta R^{3} + \\Delta^{2} R^{6}}}{6 R^{3}} : 1, \\  - \\frac{3 C_{3} + \\Delta R^{3} + 3 \\sqrt{9 C_{3}^{2} - 2 C_{3} \\Delta R^{3} + \\Delta^{2} R^{6}}}{6 R^{3}} : 1\\right\\}$"
      ],
      "text/plain": [
       "⎧                 ⎛                   ___________________________⎞       ⎛    \n",
       "⎪          3      ⎜          3       ╱     2           3    2  6 ⎟       ⎜    \n",
       "⎪3⋅C₃ - Δ⋅R      -⎝3⋅C₃ + Δ⋅R  - 3⋅╲╱  9⋅C₃  - 2⋅C₃⋅Δ⋅R  + Δ ⋅R  ⎠      -⎝3⋅C₃\n",
       "⎨───────────: 1, ──────────────────────────────────────────────────: 1, ──────\n",
       "⎪       3                                  3                                  \n",
       "⎪    3⋅R                                6⋅R                                   \n",
       "⎩                                                                             \n",
       "\n",
       "               ___________________________⎞    ⎫\n",
       "      3       ╱     2           3    2  6 ⎟    ⎪\n",
       " + Δ⋅R  + 3⋅╲╱  9⋅C₃  - 2⋅C₃⋅Δ⋅R  + Δ ⋅R  ⎠    ⎪\n",
       "────────────────────────────────────────────: 1⎬\n",
       "                    3                          ⎪\n",
       "                 6⋅R                           ⎪\n",
       "                                               ⎭"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ - \\frac{3 C_{3} + \\Delta R^{3}}{3 R^{3}} : 1, \\  \\frac{3 C_{3} - \\Delta R^{3} - 3 \\sqrt{9 C_{3}^{2} + 2 C_{3} \\Delta R^{3} + \\Delta^{2} R^{6}}}{6 R^{3}} : 1, \\  \\frac{3 C_{3} - \\Delta R^{3} + 3 \\sqrt{9 C_{3}^{2} + 2 C_{3} \\Delta R^{3} + \\Delta^{2} R^{6}}}{6 R^{3}} : 1\\right\\}$"
      ],
      "text/plain": [
       "⎧                                       ___________________________           \n",
       "⎪ ⎛          3⎞                3       ╱     2           3    2  6            \n",
       "⎪-⎝3⋅C₃ + Δ⋅R ⎠      3⋅C₃ - Δ⋅R  - 3⋅╲╱  9⋅C₃  + 2⋅C₃⋅Δ⋅R  + Δ ⋅R       3⋅C₃ -\n",
       "⎨───────────────: 1, ──────────────────────────────────────────────: 1, ──────\n",
       "⎪         3                                  3                                \n",
       "⎪      3⋅R                                6⋅R                                 \n",
       "⎩                                                                             \n",
       "\n",
       "             ___________________________   ⎫\n",
       "    3       ╱     2           3    2  6    ⎪\n",
       " Δ⋅R  + 3⋅╲╱  9⋅C₃  + 2⋅C₃⋅Δ⋅R  + Δ ⋅R     ⎪\n",
       "────────────────────────────────────────: 1⎬\n",
       "                  3                        ⎪\n",
       "               6⋅R                         ⎪\n",
       "                                           ⎭"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1be491a4b70>"
      ]
     },
     "execution_count": 1060,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(20,10))\n",
    "Rvals = np.linspace( 10*mc.a0, 1000*mc.a0, 3000 )\n",
    "potentialList = [V_0_pm_g, V_0_pm_u, V_1_g, V_1_u, V_2_g, V_2_u]\n",
    "names=[r'$0^\\pm_g$',r'$0^\\pm_u$',r'$1_g$',r'$1_u$', r'$2_g$', r'$2_u$']\n",
    "linestyles=[':','-','-.',':','-','-.',':','-','-.',':','-','-.']\n",
    "colors, _ = misc.getColors(len(potentialList), cmStr='viridis')\n",
    "\n",
    "data = [[] for _ in range(len(potentialList))]\n",
    "\n",
    "for matrixnum, (name, potentialMatrix, c_) in enumerate(zip(names, potentialList, colors)):\n",
    "    if matrixnum < 2:\n",
    "        display(potentialMatrix.eigenvals())\n",
    "    matrixFunc = sp.lambdify(R, potentialMatrix.subs(C3,Sr_C_3_Val).subs(Delta,SrDeltaVal), 'numpy')\n",
    "    for rv in Rvals:\n",
    "        data[matrixnum].append(sorted(np.linalg.eigvals(matrixFunc(rv))))\n",
    "for name, mdata, c_, linestyle in zip(names, data, colors, linestyles):\n",
    "    if len(np.array(mdata).shape) == 2 or len(np.array(mdata).shape) == 3:\n",
    "        for lineNum, lineData in enumerate(misc.transpose(mdata)):\n",
    "            ax.plot(Rvals*1e9, np.array(lineData) * 1e-9 / mc.h, label=name if lineNum == 0 else None, color=c_, linestyle=linestyle)\n",
    "    else:\n",
    "        ax.plot(Rvals*1e9, np.array(mdata) * 1e-9 / mc.h, label=name, color=c_, linestyle=linestyle)\n",
    "        \n",
    "ax.set_xlabel('Inter-nuclear distance (nm)')\n",
    "ax.set_ylabel('Energy (GHz)')\n",
    "ax.grid(alpha=0.1)\n",
    "\n",
    "ax.set_title('Full Range')\n",
    "ax.set_xlim(min(Rvals)*1e9,max(Rvals)*1e9/20)\n",
    "ax.legend(ncol=5,fontsize=14)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# P-P Molecules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1031,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|00000\\right\\rangle }, \\  {\\left|00100\\right\\rangle }, \\  {\\left|1-1110\\right\\rangle }, \\  {\\left|10000\\right\\rangle }, \\  {\\left|10100\\right\\rangle }, \\  {\\left|111-10\\right\\rangle }, \\  {\\left|2-1110\\right\\rangle }, \\  {\\left|20000\\right\\rangle }, \\  {\\left|20100\\right\\rangle }, \\  {\\left|211-10\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘00000⟩, ❘00100⟩, ❘1-1110⟩, ❘10000⟩, ❘10100⟩, ❘111-10⟩, ❘2-1110⟩, ❘20000⟩, ❘2\n",
       "0100⟩, ❘211-10⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$1_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|00110\\right\\rangle }, \\  {\\left|10110\\right\\rangle }, \\  {\\left|11000\\right\\rangle }, \\  {\\left|11100\\right\\rangle }, \\  {\\left|2-2110\\right\\rangle }, \\  {\\left|20110\\right\\rangle }, \\  {\\left|21000\\right\\rangle }, \\  {\\left|21100\\right\\rangle }, \\  {\\left|221-10\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘00110⟩, ❘10110⟩, ❘11000⟩, ❘11100⟩, ❘2-2110⟩, ❘20110⟩, ❘21000⟩, ❘21100⟩, ❘221\n",
       "-10⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$2_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|11110\\right\\rangle }, \\  {\\left|21110\\right\\rangle }, \\  {\\left|22000\\right\\rangle }, \\  {\\left|22100\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘11110⟩, ❘21110⟩, ❘22000⟩, ❘22100⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$3_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|22110\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘22110⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$0_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|00001\\right\\rangle }, \\  {\\left|00101\\right\\rangle }, \\  {\\left|1-1111\\right\\rangle }, \\  {\\left|10001\\right\\rangle }, \\  {\\left|10101\\right\\rangle }, \\  {\\left|111-11\\right\\rangle }, \\  {\\left|2-1111\\right\\rangle }, \\  {\\left|20001\\right\\rangle }, \\  {\\left|20101\\right\\rangle }, \\  {\\left|211-11\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘00001⟩, ❘00101⟩, ❘1-1111⟩, ❘10001⟩, ❘10101⟩, ❘111-11⟩, ❘2-1111⟩, ❘20001⟩, ❘2\n",
       "0101⟩, ❘211-11⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$1_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|00111\\right\\rangle }, \\  {\\left|10111\\right\\rangle }, \\  {\\left|11001\\right\\rangle }, \\  {\\left|11101\\right\\rangle }, \\  {\\left|2-2111\\right\\rangle }, \\  {\\left|20111\\right\\rangle }, \\  {\\left|21001\\right\\rangle }, \\  {\\left|21101\\right\\rangle }, \\  {\\left|221-11\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘00111⟩, ❘10111⟩, ❘11001⟩, ❘11101⟩, ❘2-2111⟩, ❘20111⟩, ❘21001⟩, ❘21101⟩, ❘221\n",
       "-11⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$2_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAAXCAYAAADqf++eAAAABHNCSVQICAgIfAhkiAAABU1JREFUeJztnVmIHEUYx3+bKIjibtSgPggmKyY+KPFBPNCQMUJMREzweNKoqC8aWBXFA5XMCoIvXvF8EBER30SWRPEAd4IaFBF8EI+NgfVAQzzw3CAe68NXzXZ6ambSX3dX9cx8P1hqmO7/dPHrSnV3dXdlpNlsYhiGYQw2i1KfG8B86u/zzLpN9/2yAPXqJ1YjXrZUuI0m5t6HuY9DCO9g7n30cr+UA/vx+WTBIs/KO4FJ4IkcFbgceBx4B/jNbeDFkjMhtqHJvAf8AGzs8btVcAxwA/AK8CWwH/gVeBe4Hv/+BXNfBhr32v11AvAc8B3wFzALPAoc1aV+eTN53Mf0DuHca9owxHU/h/Tfk8BX6QWHeFZuIUfUPNwLrAL+AL4FTqkgE2Ibmsx/wA7gKmAMaUChuAJ4GvgemAa+Bo4DLgWeBTa4deYzOXNfHI17TeYkYBdwLDCFXHGfCdwMrAfOBX7K1E2TyeM+pncI517ThmO7n2Oh/24AJyYLOp1J5OVWYAUwCtxYUSbENrSZKeBQpMGEZAa4BDmTuBK4G7gOaSzfAJchjTmLuS+Oxr0m8xTScUwAm4C7gLXAI8BK4AFP3TSZvO5jeYdw7jXtsbbuy+rsp4HdtJ9BlpkJsQ1t5i3ksjD0Ze3bwHbkaJ9mL/CM+9zw5Mx9cTTu82bGgXXIMMCTmcxW4E9gM3BEwQzkdx/LO4RxD/md1Np9WZ39sDOH7IANyBG3Dvztyn+i1qJ6BsW9L7PWlW/S3kn9jozfHg6cXTCjoY7eoTz3Gmrt3jr78phCxtAakesBci/mavf59ZgVCUS/u++UWenKmQ653a5cUTCjpU7eoVz3Gmrt3jr78tiBHM1jPaGQ5kHgVOA14I3IdQlBv7vvlBlzZacboMn3SwpmtNTJO5TrXkOt3VtnXx77gPeRm0AxmQBuQ54C2By5LqHoZ/dF9teIK/Pc49BkOlEX7xDevYao7q2zL5dR5DnZWGwBHgM+Bc4Hfo5Yl9D0o/temeRMcAw/o5n1tJkixPYO1bjXUGv31tmXxzhyOTgVafu3IC/CfYI03r2R6hGDfnR/MJkvXNlpjPdkV6bHiDUZLbG9Q3XuNdTavXX25ZGMncVo+Hciz/F+jDTefRHqEJN+c3+wmWlXrqP93+qRyAs6+5HL+SIZLTG9Q7XuNdTavXX25bEReTvvw8z3zyNjdNdWtN37kJtMHwEXAD9WtJ0600/u82T2II/xLaN9LpRJ5HntF5Dnt4tktHTyDv3vXkNd3HvxTZegYZP7AzjelecgOxxE6u0FMyG2oc0cDZyHvHadvfmSHFCreN79GuB+4F9kXo0JzzqzLNQ9wdwXR+Nek7kJef1+G9JBfQachZyVzgD3eH5Dk8nrvpt3GAz3mvZYB/deyursT0dkphl3fyAT8mSl5M2E2IY2czGwGP8l1WnICxWvepYVZbkrFyPjkD520t7Zm/viaNxrMnuAM5COaj1wEXJGtw05W/TdWNRk8rrv5h0Gw72mPdbBvZeR1Hz2DWTMaRL/RGhN5JXf5cgR0FjgZWScbikyy13CEmTSo4eAOwr8fhNz3wlzH4dO3sHcV00392lawBrcI5++Mfut+OezN/wcBlyIvH2XFb8aeRX74dCVGhLMfRy6eQdzXyW93Kfns1+TXpAexplFzuoThvFGn4ZVyPzYL3mWbUd2jlEN5j4O3byDua+SXu6T+ezbyHb2zTJrNSR8gIy5GeEx93Ew7/Ho5T49n/0B5LlB23LlLzkyRjm0XGnuw9NypbkPT8uV5r4ERuw/HDcMwxh87KUqwzCMIeB/5gr5UbCdNzIAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|11111\\right\\rangle }, \\  {\\left|21111\\right\\rangle }, \\  {\\left|22001\\right\\rangle }, \\  {\\left|22101\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘11111⟩, ❘21111⟩, ❘22001⟩, ❘22101⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$3_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|22111\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘22111⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "states = calculateBOStates(1,1,sp.S(1)/2,sp.S(1)/2)\n",
    "for key,v in states.items():\n",
    "    display(Latex(key),v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1055,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       ">>>$^1\\Sigma_g$ $0_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|00000\\right\\rangle }, \\  {\\left|10000\\right\\rangle }, \\  {\\left|20000\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘00000⟩, ❘10000⟩, ❘20000⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Sigma_g$ $0_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|00100\\right\\rangle }, \\  {\\left|10100\\right\\rangle }, \\  {\\left|20100\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘00100⟩, ❘10100⟩, ❘20100⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Pi_g$ $0_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|1-1110\\right\\rangle }, \\  {\\left|111-10\\right\\rangle }, \\  {\\left|2-1110\\right\\rangle }, \\  {\\left|211-10\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘1-1110⟩, ❘111-10⟩, ❘2-1110⟩, ❘211-10⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Sigma_g$ $1_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoMAAAAXCAYAAABwBkXyAAAABHNCSVQICAgIfAhkiAAABrRJREFUeJztnUmoHFUUhr8MgigmUYO6EEwiJi6UuBAHNOSZQExETHBYaVTUjQaiojigkn6C4sYpjguRIOJO5JEoDmA6OKCI4EI0ZoDnQJQ44PhicIiLU+2r9Kvqzrl169atqvNBc5uuuq/P/f86VedVVd+a1ul0MAzDMAzDMNrJ9NT7EeBA6rW9b91O8vm8AHEZkyxBdF9X8vd0MH/7Me2bTQh/O5i3WZj2zcX2m9UxTPu5HFznHegtmJ6x8jZgFHhSGcSJwPPAHmA/MA48Bhztqc/lwBPAO8CvyCBeVMZYBi5xacb9HvA9sNpPuM5o/dWu76Jj07V33eZDaF82IcbeBn9D5ZU2riq1Pxa4AXgF2AXsA34B3gWuJ/u42MOOWeZtD62OMeTVBFLfjQJfphfMzFi5i1TcGk4G3geOA8aQs4pnATcDK4HzgB8L9rkXWAz8DnwDnKqMsSy0cWnH/S+wBbgKmI1s2KHRxuyyPbj423TtXTQJpX3ZhBh7G/wNkVcucVWp/RXAM8C3wFbgK+B44FLgOWBVss6Bvn52zDJv02h1jCGvJpis70aAk3oLBlXJGp5Ogl0PrAHuApYBjwKLgAc89LkVWAjMAm70FLcPtHG5aDUGHIZsyFWgjdlljC7+Nl17F01CaV82ocbedH9D5JVLXFCd9juAS5AzLlcCdwPXIQfnr4HLkOKhHztmmbdptDpGnVc+isEFwArk1OVTfcs2AH8Aa4EjC/bZCuxkakVfNZq4XMYN8BZyuruK0+7amF3H6OJv07XXahJS+7IJNfam+1t2XrnGBdVp/zawGTmLkuY74Nnk/UjfMjtmmbdF95tR55WPYnBZ0r7JVAN+Q65hHwGcU7BPE3Ad9wRi8Cqk4g+JNuZYva2j9lpi1T4E5q/llg/+Stq/+z6PVfuyMW9bklc+isFFSbsjZ/nOpF1YsE8TKDLuMeQegBHPMQ1DG3Os3tZRey2xah8C89dyqygzgauT96/3LYtV+7Ixb1uSVz6KwdlJm3eTaO/zOQX7NIEi496C/HcQ+rS7NuZYva2j9lpi1T4E5q/lVlEeAk4DXgPe6FsWq/ZlY962JK98/YBkENOSVnPfhEufQ2GcqXPsDHqFngZg0Lj3Ah8gN8fGhNarsrwtSh2119LWvALzt0rqoP164Dbk15prHfq3NbfM2+rwqn3W1DJaetXp7Jzls/rWc+3jg93An4r193j+/qLjnoXMTxQSbcxVeTuMOmqvpa15BeYvWG65sg54HPgMWA78lLFOW3PLvG1JXvkoBr9I2rzr6ackbfq6t0sfHyz3/Pe0FBn3AuQ094O+gxqCNuaqvB1GHbXX0ta8AvMXLLdcuAWZpuNTZDvem7NeW3PLvG1JXvm4TLw1aVdk/L2jkEkR9yGnLIv0aQJFxt279j9WTmi5aGOO1ds6aq8lVu1DYP5abmm5EykWPgEuIL9YgHi1LxvztiV55aMY3I389HkeU5+HN4rMgfMCMidOkT5NoMi4VyOzqn+UsWwTct/AtX7CPAhtzLF6W0fttcSqfQjK8HcT8XgL8fpbR+3vQ35U8DFy1uiHIevHqn3Z1HG/2RRvy9I+Ex+XiQFuQh6ZshER/3PgbKQi3wHc46HPmuQFcELSnotsVCCG3154JHq0cblodQxwPvI4naybRXtFff/8Sb7QxuwyRhd/m669iyahtC+bUGMf5G/ZeRVijCHyyiUuqE77a4D7gX+Q58Suz1hnnMnx9rBjVvz7zVDegl7HGPIqF1/F4G7gTMSElcBFSFW6Ealgs27a1PY5AzE6zYLkBfLQ5SoSSxuXi1YXAzPIP+V7OjIJ5av68A8JbcwuY3Txt+nau2gSSvuyCTX2Qf6WnVchxhgir1ziguq0n5+0M5D7yrLYxtSCwY5Z8e83Q3kLeh1jyKtcpnU6nd77EeQa9SiTDzJO00EegTIfqayNcLyM3DcwF9jft2wO8qDqh4E7CnxHB/M3C9O+2eT5a96Wj2nfXGy/WR2DtE/TBZaSTFGTdc/gBuTU4na/8RmOHA5ciMyanmXsEuQxO4+EDKolmPbNZpC/5m25mPbNxfab1TFM+7lMzkm5NL0gfZl4HDkr2GPYTZdGGBYDu4CXcpZvRjYAwz+mfbMZ5K95Wy6mfXOx/WZ1DNN+goPrvP/pLwY7PqMyvPAhcq+BER7TvtmYv9Vh2jcX87Y6hmk/QU6dp/kBSTdpf1b0MepDN2nN3/B0k9a0bx7dpDVvw9NNWtO+mXST1vz1QPoHJIZhGIZhGEbL8DHptGEYhmEYhlFT/gPc1xHVBRN1YgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|001-10\\right\\rangle }, \\  {\\left|00110\\right\\rangle }, \\  {\\left|101-10\\right\\rangle }, \\  {\\left|10110\\right\\rangle }, \\  {\\left|201-10\\right\\rangle }, \\  {\\left|20110\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘001-10⟩, ❘00110⟩, ❘101-10⟩, ❘10110⟩, ❘201-10⟩, ❘20110⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^1\\Pi_g$ $1_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|1-1000\\right\\rangle }, \\  {\\left|11000\\right\\rangle }, \\  {\\left|2-1000\\right\\rangle }, \\  {\\left|21000\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘1-1000⟩, ❘11000⟩, ❘2-1000⟩, ❘21000⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Pi_g$ $1_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|1-1100\\right\\rangle }, \\  {\\left|11100\\right\\rangle }, \\  {\\left|2-1100\\right\\rangle }, \\  {\\left|21100\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘1-1100⟩, ❘11100⟩, ❘2-1100⟩, ❘21100⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Delta_g$ $1_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|2-2110\\right\\rangle }, \\  {\\left|221-10\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘2-2110⟩, ❘221-10⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Pi_g$ $2_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|1-11-10\\right\\rangle }, \\  {\\left|11110\\right\\rangle }, \\  {\\left|2-11-10\\right\\rangle }, \\  {\\left|21110\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘1-11-10⟩, ❘11110⟩, ❘2-11-10⟩, ❘21110⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^1\\Delta_g$ $2_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|2-2000\\right\\rangle }, \\  {\\left|22000\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘2-2000⟩, ❘22000⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Delta_g$ $2_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|2-2100\\right\\rangle }, \\  {\\left|22100\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘2-2100⟩, ❘22100⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Delta_g$ $3_g$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|2-21-10\\right\\rangle }, \\  {\\left|22110\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘2-21-10⟩, ❘22110⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       ">>>$^1\\Sigma_u$ $0_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|00001\\right\\rangle }, \\  {\\left|10001\\right\\rangle }, \\  {\\left|20001\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘00001⟩, ❘10001⟩, ❘20001⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Sigma_u$ $0_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|00101\\right\\rangle }, \\  {\\left|10101\\right\\rangle }, \\  {\\left|20101\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘00101⟩, ❘10101⟩, ❘20101⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Pi_u$ $0_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|1-1111\\right\\rangle }, \\  {\\left|111-11\\right\\rangle }, \\  {\\left|2-1111\\right\\rangle }, \\  {\\left|211-11\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘1-1111⟩, ❘111-11⟩, ❘2-1111⟩, ❘211-11⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Sigma_u$ $1_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|001-11\\right\\rangle }, \\  {\\left|00111\\right\\rangle }, \\  {\\left|101-11\\right\\rangle }, \\  {\\left|10111\\right\\rangle }, \\  {\\left|201-11\\right\\rangle }, \\  {\\left|20111\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘001-11⟩, ❘00111⟩, ❘101-11⟩, ❘10111⟩, ❘201-11⟩, ❘20111⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^1\\Pi_u$ $1_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAawAAAAXCAYAAABXsnuuAAAABHNCSVQICAgIfAhkiAAABWpJREFUeJztnVmIHEUYx3+bRBDF3ahBfRBMVkx8UOKDeKAhYwIxETHB40mjor5oYFUUD1QyKyi+eMXzQSSI+CayJIoHuBM8UETwQTw2LowHUeKB50bxWB++aqYzU93bVX33fD8Yapjq6vr4/7unqqurq0fa7TaKoiiKUnUWhb63gPnQ57O+bdvm9+UFxKX0WIPovi3netqov/2o9s2mCH/bqLc24rRfxsFt0XyQsciy8R5gEnjcofJLgceAt4BfTQXPO5TPA9+YjgeeBfYBfwFd4BHgyIzKuMb1DvA9sDlB7HnhGrNqn56jgeuAl4AvgAPAL8DbwLXYz92i8PE3b2994qqjv8Og/RzSBk0CX4Yzllg27iC9AhfuBlYDvwPfACc7ls8Dn5hOBN4FjgGmkKvMM4AbgY3AOcCPKcu4xvUfsBu4AhhDDuqicY1ZtU/PZcBTwLfANPAVcCxwMfAMsMlsMx+1gxxx1bEIb33iqqO/w6D9HL02qAWcEGRk1Uu7GVgJjALXZ7TPtPjE9CRi0gSwBbgDWAc8DKwC7sugjE9cU8AhyEFcBq4xq/bpmQEuQnq6lwN3AtcgfwRfA5cgf25l4KpjEd76xAX183eotc+qwZoG9lJOby8K15jGgQ3Ipe8TfXnbgT+ArcDhKcv4aPUGMmRQ1rCga8yqfXreBHYhPdEw3wFPm++tIgMK4aJjUd66xhVQN3+HWvsyx8GrxjqTvs7gQfQbMuZ6GHBWyjI+zCHmbkJ6JE1DtXfjb5P+U2oUyaiyt9BsfxunvTZYPVaZdCYif69JV6Ys48sUMtbbymBfVUO1T84S4Erz/dUyA0lI1b2F5vrbOO21weoxZtKoG6/B70tTlvFlN9LjKXO2YF6o9sl5ADgFeAV4reRYklB1b6G5/jZO+yo1WF0G597HfYqeNj9iUpcxWp8yUewH3kNu1A4bqr0wAdyCzNramrBMFz2vFqLO/qahdtrbprWXxSzwp8P2+zKuP+g5jEXkj/Zt51smDaPIMw5NQ7VfmG3Ao8AnwHrgp4Tl9LxKRl39jaNx2lepwVpfcv2fmzRqbPYkk4bHdn3K+DKODBXcn8G+qoZqH89NyJTij5HzZL9DWT2vFqbO/sbROO2rNCRYNtMm3cCgLkcgD8sdQC5f05TxJRjjncpgX1VDtY/mduTP7CPgPLL7MyuKqnsLzfW3cdprg9VjFpnKuZzB9a0mkecOnkOeQ0hTxpfNyFPxH1jydiJjyldnUE8ZqPZ27kFuwn+I9Lx/yKGOvKm6txDt707yPa/y9rfO2lvJakhwi/kAHGfSsxHDQYy4NaO68ozpBmRJkh3IAfQpcCbS85kB7rLU41rGJ66jgHORJVtsNzuDjkdez+W4xqzap+cq4F7gX2R9tgnLNl16sReJq45FeOsTF8T7m+d55evvsGhvJasG6zTEgDDj5gOygGHRDZZPTLPA6ciBtBG4AGn9dyC9C9uNUNcyPnFdCCwm+rL5VOShvpcj8tPiGrNqn54VJl2M3OOwsYdyGixXHYvw1icuiPc3z/PK199h0d7KSOh9WC1k/HIS++K3bWRpjhVIy68Ux4vImPIyZOXkMEuRhSgfBG5LUUcb9deGat9sovxVb/Mn7twK6ABrMdPpbfewtmN/H5ZSDocC5yNPvdtMXYMs5fJQkUENCap9s4nzV73Nlzjtw+/DWhvOCA8JdpGrq4A63uBtIquR9+W8EJG/CzFfyR7VvtnE+ave5kuc9sH7sAbob7DaWUelpOZ9ZHxYKR7Vvtmov+URp334fVgH4TLpomPSnx3KKPWhY1L1t3g6JlXtm0fHpOptBoQnXSiKoihKZdEHhxVFUZRa8D+oKVVUY3WYGgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|1-1001\\right\\rangle }, \\  {\\left|11001\\right\\rangle }, \\  {\\left|2-1001\\right\\rangle }, \\  {\\left|21001\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘1-1001⟩, ❘11001⟩, ❘2-1001⟩, ❘21001⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Pi_u$ $1_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|1-1101\\right\\rangle }, \\  {\\left|11101\\right\\rangle }, \\  {\\left|2-1101\\right\\rangle }, \\  {\\left|21101\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘1-1101⟩, ❘11101⟩, ❘2-1101⟩, ❘21101⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Delta_u$ $1_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO4AAAAXCAYAAAAMc3PzAAAABHNCSVQICAgIfAhkiAAABABJREFUeJzt3EuIHEUcx/HPxgieoqigB0HNQTwo8SoYshJQAmLEx8kn6kUCQVEUIZJZD+JFRRT04MGDeBNZEkURzAQVFBE8iIgPWB+oxCi+WBUf66F6SGe3d3aqp6u6J/QXmh62qvb/39+vqqequ2vnBoOBnp6e2WJT6fM8VkrHJ6vqDoqfn5chr55jbBd035M4zkDvbxuM8/dMx4/JlVHBporKh7GApycMfAbuxMv4HH/gF7yNO9aJkZq6OV2Pp/AWfhWEemGDWLFtYuu/gx+we4M8UhGrZU7tU5OjP4zzd1kYiwv4slywuaLyULj6TsoNeAbf4RC+wlm4Fs9hV1FnZb1fkIC6Oe3DNvyOb3DhBLFi28TW/w8HcRNOFQZBTmK1zKl9anL0h3H+Ljs2Fudx7qigiW/DT3E1zsGNeBC3Fwl/jesE03JSN6d7cAG24K4JY8W2qRNjEScLnT43sVrm1D41OfoDNfxtYuC+iQPClaPM93i2+DzfQJwY6uZ0CJ+Jmx3EtqkT4w1hytnGdDlWy5zapyZHf6CGv6nXn38X538Sx4mhizltxLJg7i7hytwVYrWcRe1zEO1vyoG7GbcUn19LGCeGLuY0KYvCGmi+5TxGxGo5y9rnIMrflAP3UVyEV/F6wjgxdDGnSTkoTD/buru8mlgtZ1n7HET5m2rg7sW9wrPgmydss2TtM6txR+yjgjo5dYkjeFe48dM2sVrm0n5J2j6Ukih/qx4HTcsePImPsRM/TdjuC/wZEefbDDl1jS3Cs8E2idUyp/Yp+1AOJva36YF7N57AR4JJRyLa7mw4lxHT5NQltgpTzUdazCFWy9zap+pDOYjyt8mp8gOCSR/ict0YIF3MqS6jtc9iS/FjtTyRtM9BlL9NDdyHhJsPHwhXvaMN/d5p6GJO07BbeBvp/Yqy54U1222JYsdqeaJpn4Nx/q6hianyrXgY/wrvZ+6tqLMkdK5c1M3pmuKAs4vzpaV6R3HflG3qxDgdlwmvDFY92B9dgFM8H43VMqf2qcnRH9jY3zU0MXDPL84nCWuaKg7LO3Dr5nSJ0PHKbC0Owoveq0WPbVMnxlXC37LeNOpi/IZX1imfhlgtc2qfmhz9gY39XcNcaT/uvPC61oLqTQYD7BeMWZo0QE8jvIQrhG1ef60qOw0/4jHcP0WMgd7fthjn74ghdmCO6jXuftX7cXva4RRcKbxtVGXqduFVwsdzJtXTGOP8Le/H3VEuKE+Vl4Rv2xH9DYVusE3Y1/riOuUHBPN7ZpNx/o72465h9cAdNJ1Vz9S8J6ybek5Mxvlb3o97HDE3p4bF+eeINj2zw7A49/7OALEDd5gmjZ4OMNT7OzO08f+genp6puR/cceo35KbMUsAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|2-2111\\right\\rangle }, \\  {\\left|221-11\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘2-2111⟩, ❘221-11⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Pi_u$ $2_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|1-11-11\\right\\rangle }, \\  {\\left|11111\\right\\rangle }, \\  {\\left|2-11-11\\right\\rangle }, \\  {\\left|21111\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘1-11-11⟩, ❘11111⟩, ❘2-11-11⟩, ❘21111⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^1\\Delta_u$ $2_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|2-2001\\right\\rangle }, \\  {\\left|22001\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘2-2001⟩, ❘22001⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Delta_u$ $2_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|2-2101\\right\\rangle }, \\  {\\left|22101\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘2-2101⟩, ❘22101⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       ">>>$^3\\Delta_u$ $3_u$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ {\\left|2-21-11\\right\\rangle }, \\  {\\left|22111\\right\\rangle }\\right]$"
      ],
      "text/plain": [
       "[❘2-21-11⟩, ❘22111⟩]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n"
     ]
    }
   ],
   "source": [
    "states = calculateBOStates(1,1,sp.S(1)/2,sp.S(1)/2)\n",
    "for key, val in states.items():\n",
    "    #display(Latex(key))\n",
    "    for key2, states in val.items():\n",
    "        display(Latex('>>>'+key2+' '+key),states)\n",
    "    print(\"=============================================\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1056,
   "metadata": {},
   "outputs": [],
   "source": [
    "L1S1ToJ = LStoJOperator(spin1, spin1)\n",
    "fs_1_p5 = fineStructureInteraction(spin1, spinP5)\n",
    "BOto2_s1e1_s2e0 = BoToTwoAtomStatesOperator(s1=sp.S(1)/2, s2=sp.S(1)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 963,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0^\\pm_g$:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3} & \\frac{\\sqrt{2} \\Delta}{3} & 0\\\\\\frac{\\sqrt{2} \\Delta}{3} & - \\frac{2 C_{3}}{R^{3}} & 0\\\\0 & 0 & \\frac{C_{3}}{R^{3}} - \\frac{\\Delta}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C₃   Δ   √2⋅Δ         ⎤\n",
       "⎢── - ─   ────     0   ⎥\n",
       "⎢ 3   3    3           ⎥\n",
       "⎢R                     ⎥\n",
       "⎢                      ⎥\n",
       "⎢ √2⋅Δ   -2⋅C₃         ⎥\n",
       "⎢ ────   ──────    0   ⎥\n",
       "⎢  3        3          ⎥\n",
       "⎢          R           ⎥\n",
       "⎢                      ⎥\n",
       "⎢                C₃   Δ⎥\n",
       "⎢  0       0     ── - ─⎥\n",
       "⎢                 3   3⎥\n",
       "⎣                R     ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "State0mg_3Sigmg = OKet(1,0,1,0,g)\n",
    "State3Pig1 = OKet(1,1,1,-1,g)\n",
    "State3Pig2 = OKet(1,-1,1,1,g)\n",
    "State0mg_3Pig = 1/sp.sqrt(2)*(State3Pig1+State3Pig2)\n",
    "State0pg_3Pig = 1/sp.sqrt(2)*(State3Pig1-State3Pig2)\n",
    "\n",
    "V_0_pm_g = (createBOMatrix(State3Pig1, State0mg_3Sigmg, State3Pig1) \n",
    "            + createMovrePichlerMatrix( State0mg_3Pig, State0mg_3Sigmg, State0pg_3Pig, fineStructureOperator=fs_1_1, offset=sp.S(0), \n",
    "                                        BOto2AtomOperator=BOto2_s1e1_s2e0, LStoJOperator=L1S1ToJ, subs={A:Delta/3} ))\n",
    "display(Latex('$0^\\pm_g$:'), V_0_pm_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}