{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating dipole matrix elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from rydstate.rydberg_state import RydbergStateAlkali"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numerov radial matrix element: -137.76904105892473 bohr\n",
      "Numerov angular matrix element: 0.23936536824085952\n",
      "Numerov dipole matrix element: -67.49277058938209 bohr * elementary_charge\n"
     ]
    }
   ],
   "source": [
    "state_i = RydbergStateAlkali(\"Rb\", 60, 2, j=3 / 2, m=1 / 2)\n",
    "state_f = RydbergStateAlkali(\"Rb\", 60, 3, j=5 / 2, m=1 / 2)\n",
    "\n",
    "kappa = 1\n",
    "radial = state_i.radial.calc_matrix_element(state_f.radial, k_radial=1)\n",
    "angular = state_i.angular.calc_matrix_element(state_f.angular, \"spherical\", kappa=kappa, q=0)\n",
    "prefactor = np.sqrt(4 * np.pi / (2 * kappa + 1))\n",
    "print(f\"Numerov radial matrix element: {radial}\")\n",
    "print(f\"Numerov angular matrix element: {angular}\")\n",
    "\n",
    "dipole = state_i.calc_matrix_element(state_f, \"electric_dipole\", q=0)\n",
    "print(f\"Numerov dipole matrix element: {dipole}\")\n",
    "\n",
    "assert np.isclose(dipole.magnitude, (prefactor * radial * angular).magnitude), (\n",
    "    f\"{dipole} != {prefactor * radial * angular}\"\n",
    ")"
   ]
  }
 ],
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