{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyOR Quantum\n",
    "## Author: Vineeth Thalakottoor\n",
    "## Introduction to Coupled States"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the source path\n",
    "SourcePath = '/media/HD2/Vineeth/PostDoc_Simulations/Github/PyOR_V1/PyOR_Combined/PyOR/Source_Doc'\n",
    "\n",
    "# Add source path\n",
    "import sys\n",
    "sys.path.append(SourcePath)\n",
    "\n",
    "# Import PyOR package\n",
    "from PyOR_QuantumSystem import QuantumSystem as QunS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the spin system\n",
    "Spin_list = {\"A\" : \"H1\",\"B\" : \"H1\",\"C\" : \"H1\",\"D\" : \"H1\"}\n",
    "QS = QunS(Spin_list,PrintDefault=False)\n",
    "\n",
    "# initialize the system\n",
    "QS.Initialize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Four uncouple spins \n",
    "X1 = QS.States_Coupled([{\"A\": 1/2},{\"B\": 1/2},{\"C\": 1/2},{\"D\": 1/2}])\n",
    "X1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Four uncouple spins\n",
    "X2 = QS.States_Coupled([{\"A\": -1/2},{\"B\": -1/2},{\"C\": -1/2},{\"D\": -1/2}])\n",
    "X2.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# State of sub system A\n",
    "X3 = QS.States_Coupled([{\"A\": 1/2}])\n",
    "X3.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# State of sub system A\n",
    "X4 = QS.States_Coupled([{\"A\": -1/2}])\n",
    "X4.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# State of uncoupled sub system A and B\n",
    "X5 = QS.States_Coupled([{\"A\": 1/2},{\"B\": 1/2}])\n",
    "X5.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\-0.707106781186547\\\\0.707106781186548\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                 0],\n",
       "[-0.707106781186547],\n",
       "[ 0.707106781186548],\n",
       "[                 0]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# State of coupled sub system A and B\n",
    "X6 = QS.States_Coupled([{\"New\" : {\"l\" : 0, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2}}])\n",
    "X6.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# State of coupled sub system A and B\n",
    "X7 = QS.States_Coupled([{\"New\" : {\"l\" : 1, \"m\" : 1, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2}}])\n",
    "X7.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0.707106781186548\\\\0.707106781186547\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                0],\n",
       "[0.707106781186548],\n",
       "[0.707106781186547],\n",
       "[                0]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# State of coupled sub system A and B\n",
    "X8 = QS.States_Coupled([{\"New\" : {\"l\" : 1, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2}}])\n",
    "X8.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# State of coupled sub system A and B\n",
    "X9 = QS.States_Coupled([{\"New\" : {\"l\" : 1, \"m\" : -1, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2}}])\n",
    "X9.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# One uncoupled (A) spin and Two coupled spins (B and C)\n",
    "# State of coupled sub system A and B\n",
    "X10 = QS.States_Coupled([{\"A\": 1/2},{\"New\" : {\"l\" : 1, \"m\" : 1, \"Select_l\" : 0},\"Old\" : {\"B\": 1/2,\"C\": 1/2}}])\n",
    "X10.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0.707106781186548\\\\0.707106781186547\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                0],\n",
       "[0.707106781186548],\n",
       "[0.707106781186547],\n",
       "[                0],\n",
       "[                0],\n",
       "[                0],\n",
       "[                0],\n",
       "[                0]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# One uncoupled (A) spin and Two coupled spins (B and C)\n",
    "# State of coupled sub system A and B\n",
    "X11 = QS.States_Coupled([{\"A\": 1/2},{\"New\" : {\"l\" : 1, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"B\": 1/2,\"C\": 1/2}}])\n",
    "X11.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\1.0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# One uncoupled (A) spin and Two coupled spins (B and C)\n",
    "# State of coupled sub system A and B\n",
    "X12 = QS.States_Coupled([{\"A\": 1/2},{\"New\" : {\"l\" : 1, \"m\" : -1, \"Select_l\" : 0},\"Old\" : {\"B\": 1/2,\"C\": 1/2}}])\n",
    "X12.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\-0.707106781186547\\\\0.707106781186548\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                 0],\n",
       "[-0.707106781186547],\n",
       "[ 0.707106781186548],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# One uncoupled (A) spin and Two coupled spins (B and C)\n",
    "# State of coupled sub system A and B\n",
    "X13 = QS.States_Coupled([{\"A\": 1/2},{\"New\" : {\"l\" : 0, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"B\": 1/2,\"C\": 1/2}}])\n",
    "X13.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0.5\\\\-0.5\\\\0\\\\0\\\\-0.5\\\\0.5\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[ 0.5],\n",
       "[-0.5],\n",
       "[   0],\n",
       "[   0],\n",
       "[-0.5],\n",
       "[ 0.5],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Two pair of coupled system A and B coupled, and C and D coupled\n",
    "X14 = QS.States_Coupled([{\"New\" : {\"l\" : 0, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2}},{\"New\" : {\"l\" : 0, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"C\": 1/2,\"D\": 1/2}}])\n",
    "X14.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\-0.707106781186547\\\\0\\\\0\\\\0\\\\0.707106781186548\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[-0.707106781186547],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[ 0.707106781186548],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0],\n",
       "[                 0]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Two pair of coupled system A and B coupled, and C and D coupled\n",
    "X14 = QS.States_Coupled([{\"New\" : {\"l\" : 0, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2}},{\"New\" : {\"l\" : 1, \"m\" : 1, \"Select_l\" : 0},\"Old\" : {\"C\": 1/2,\"D\": 1/2}}])\n",
    "X14.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\-0.5\\\\0.5\\\\0\\\\0\\\\-0.5\\\\0.5\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[-0.5],\n",
       "[ 0.5],\n",
       "[   0],\n",
       "[   0],\n",
       "[-0.5],\n",
       "[ 0.5],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0],\n",
       "[   0]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Two pair of coupled system A and B coupled, and C and D coupled\n",
    "X15 = QS.States_Coupled([{\"New\" : {\"l\" : 1, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2}},{\"New\" : {\"l\" : 0, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"C\": 1/2,\"D\": 1/2}}])\n",
    "X15.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# All spins are coupled\n",
    "X16 = QS.States_Coupled([{\"New\" : {\"l\" : 2, \"m\" : 2, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2, \"C\": 1/2,\"D\": 1/2}}])\n",
    "X16.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0.5\\\\0.5\\\\3.23864880886297 \\cdot 10^{-16}\\\\0.5\\\\0\\\\0\\\\2.02888199778559 \\cdot 10^{-16}\\\\0.5\\\\0\\\\0\\\\2.02888199778559 \\cdot 10^{-16}\\\\0\\\\2.02888199778559 \\cdot 10^{-16}\\\\1.46071672408528 \\cdot 10^{-16}\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                   0],\n",
       "[                 0.5],\n",
       "[                 0.5],\n",
       "[3.23864880886297e-16],\n",
       "[                 0.5],\n",
       "[                   0],\n",
       "[                   0],\n",
       "[2.02888199778559e-16],\n",
       "[                 0.5],\n",
       "[                   0],\n",
       "[                   0],\n",
       "[2.02888199778559e-16],\n",
       "[                   0],\n",
       "[2.02888199778559e-16],\n",
       "[1.46071672408528e-16],\n",
       "[                   0]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# All spins are coupled\n",
    "X17 = QS.States_Coupled([{\"New\" : {\"l\" : 2, \"m\" : 1, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2, \"C\": 1/2,\"D\": 1/2}}])\n",
    "X17.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\-4.44437010144091 \\cdot 10^{-16}\\\\-3.51129910970437 \\cdot 10^{-16}\\\\0.408248290463863\\\\-2.31737691712037 \\cdot 10^{-16}\\\\0.408248290463863\\\\0.408248290463863\\\\-4.86980591674165 \\cdot 10^{-17}\\\\-2.21369385562875 \\cdot 10^{-16}\\\\0.408248290463863\\\\0.408248290463863\\\\-5.11444620266011 \\cdot 10^{-18}\\\\0.408248290463863\\\\5.38125053700757 \\cdot 10^{-17}\\\\-2.65506637475496 \\cdot 10^{-31}\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                    0],\n",
       "[-4.44437010144091e-16],\n",
       "[-3.51129910970437e-16],\n",
       "[    0.408248290463863],\n",
       "[-2.31737691712037e-16],\n",
       "[    0.408248290463863],\n",
       "[    0.408248290463863],\n",
       "[-4.86980591674165e-17],\n",
       "[-2.21369385562875e-16],\n",
       "[    0.408248290463863],\n",
       "[    0.408248290463863],\n",
       "[-5.11444620266011e-18],\n",
       "[    0.408248290463863],\n",
       "[ 5.38125053700757e-17],\n",
       "[-2.65506637475496e-31],\n",
       "[                    0]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# All spins are coupled\n",
    "X18 = QS.States_Coupled([{\"New\" : {\"l\" : 2, \"m\" : 0, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2, \"C\": 1/2,\"D\": 1/2}}])\n",
    "X18.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0.866025403784439\\\\-0.288675134594813\\\\-1.8698347616077 \\cdot 10^{-16}\\\\-0.288675134594813\\\\0\\\\0\\\\-1.56855423838949 \\cdot 10^{-16}\\\\-0.288675134594813\\\\0\\\\0\\\\-1.56855423838949 \\cdot 10^{-16}\\\\0\\\\-1.56855423838949 \\cdot 10^{-16}\\\\-2.59786491544157 \\cdot 10^{-16}\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                    0],\n",
       "[    0.866025403784439],\n",
       "[   -0.288675134594813],\n",
       "[ -1.8698347616077e-16],\n",
       "[   -0.288675134594813],\n",
       "[                    0],\n",
       "[                    0],\n",
       "[-1.56855423838949e-16],\n",
       "[   -0.288675134594813],\n",
       "[                    0],\n",
       "[                    0],\n",
       "[-1.56855423838949e-16],\n",
       "[                    0],\n",
       "[-1.56855423838949e-16],\n",
       "[-2.59786491544157e-16],\n",
       "[                    0]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# All spins are coupled\n",
    "X19 = QS.States_Coupled([{\"New\" : {\"l\" : 1, \"m\" : 1, \"Select_l\" : 0},\"Old\" : {\"A\": 1/2,\"B\": 1/2, \"C\": 1/2,\"D\": 1/2}}])\n",
    "X19.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0.0351327291507096\\\\0.790017233330623\\\\-5.82022219644816 \\cdot 10^{-16}\\\\-0.543346216784993\\\\-3.0661718775136 \\cdot 10^{-16}\\\\2.08604874259664 \\cdot 10^{-16}\\\\-1.99881058322943 \\cdot 10^{-16}\\\\-0.281803745696339\\\\-2.19085773391869 \\cdot 10^{-16}\\\\1.43172975832302 \\cdot 10^{-16}\\\\1.37003078565815 \\cdot 10^{-18}\\\\6.95202190332097 \\cdot 10^{-16}\\\\1.79421197963676 \\cdot 10^{-16}\\\\-1.05389615645798 \\cdot 10^{-17}\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                    0],\n",
       "[   0.0351327291507096],\n",
       "[    0.790017233330623],\n",
       "[-5.82022219644816e-16],\n",
       "[   -0.543346216784993],\n",
       "[ -3.0661718775136e-16],\n",
       "[ 2.08604874259664e-16],\n",
       "[-1.99881058322943e-16],\n",
       "[   -0.281803745696339],\n",
       "[-2.19085773391869e-16],\n",
       "[ 1.43172975832302e-16],\n",
       "[ 1.37003078565815e-18],\n",
       "[ 6.95202190332097e-16],\n",
       "[ 1.79421197963676e-16],\n",
       "[-1.05389615645798e-17],\n",
       "[                    0]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# All spins are coupled\n",
    "X20 = QS.States_Coupled([{\"New\" : {\"l\" : 1, \"m\" : 1, \"Select_l\" : 1},\"Old\" : {\"A\": 1/2,\"B\": 1/2, \"C\": 1/2,\"D\": 1/2}}])\n",
    "X20.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\-0.00564176435583433\\\\-0.168178055755344\\\\1.79018853220595 \\cdot 10^{-15}\\\\-0.604674375164066\\\\-1.35315959328948 \\cdot 10^{-16}\\\\1.38539816933986 \\cdot 10^{-16}\\\\6.22715665337022 \\cdot 10^{-16}\\\\0.778494195275245\\\\-2.32860407194975 \\cdot 10^{-16}\\\\8.98882211462371 \\cdot 10^{-17}\\\\-3.88900867887732 \\cdot 10^{-16}\\\\-1.70257142184444 \\cdot 10^{-15}\\\\-3.96593278267651 \\cdot 10^{-16}\\\\1.69239165700711 \\cdot 10^{-18}\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                    0],\n",
       "[ -0.00564176435583433],\n",
       "[   -0.168178055755344],\n",
       "[ 1.79018853220595e-15],\n",
       "[   -0.604674375164066],\n",
       "[-1.35315959328948e-16],\n",
       "[ 1.38539816933986e-16],\n",
       "[ 6.22715665337022e-16],\n",
       "[    0.778494195275245],\n",
       "[-2.32860407194975e-16],\n",
       "[ 8.98882211462371e-17],\n",
       "[-3.88900867887732e-16],\n",
       "[-1.70257142184444e-15],\n",
       "[-3.96593278267651e-16],\n",
       "[ 1.69239165700711e-18],\n",
       "[                    0]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# All spins are coupled\n",
    "X21 = QS.States_Coupled([{\"New\" : {\"l\" : 1, \"m\" : 1, \"Select_l\" : 2},\"Old\" : {\"A\": 1/2,\"B\": 1/2, \"C\": 1/2,\"D\": 1/2}}])\n",
    "X21.matrix"
   ]
  }
 ],
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