{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import k3d\n",
    "import numpy as np\n",
    "import scipy.special\n",
    "import scipy.misc\n",
    "\n",
    "r = lambda x,y,z: np.sqrt(x**2+y**2+z**2)\n",
    "theta = lambda x,y,z: np.arccos(z/r(x,y,z))\n",
    "phi = lambda x,y,z: np.arctan(y/x)\n",
    "\n",
    "a0 = 1.\n",
    "R = lambda r,n,l: (2*r/n/a0)**l * np.exp(-r/n/a0) * scipy.special.genlaguerre(n-l-1,2*l+1)(2*r/n/a0)\n",
    "WF = lambda r,theta,phi,n,l,m: R(r,n,l) * scipy.special.sph_harm(m,l,phi,theta)\n",
    "absWF = lambda r,theta,phi,n,l,m: abs(WF(r,theta,phi,n,l,m))**2\n",
    "N=100j\n",
    "a = 200.0\n",
    "x,y,z = np.ogrid[-a:a:N,-a:a:N,-a:a:N]\n",
    "x = x.astype(np.float32)\n",
    "y = y.astype(np.float32)\n",
    "z = z.astype(np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "orbital = absWF(r(x,y,z),theta(x,y,z),phi(x,y,z),1,0,0) # 1s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot = k3d.plot()\n",
    "plot.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot.grid_auto_fit = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "E = 10\n",
    "volume_animation = {}\n",
    "label_animation = {}\n",
    "i = 0\n",
    "\n",
    "for l in range(E):\n",
    "    print(l, '/', E-1, end='\\r')\n",
    "    for m in range(-l,l+1):\n",
    "        psi2 = absWF(r(x, y, z), theta(x, y, z), phi(x, y, z), E, l, m)\n",
    "        \n",
    "        volume_animation[str(i)] =  (psi2/np.max(psi2))\n",
    "        label_animation[str(i)] = 'n=%d \\quad l=%d \\quad m=%d' % (E,l,m)\n",
    "        \n",
    "        i += 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot += k3d.text2d(label_animation, (0.,0.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "plot += k3d.volume(volume_animation, color_map=k3d.colormaps.basic_color_maps.CoolWarm, \n",
    "                   color_range=(0.0,0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.array(volume_animation).tolist()['0'].dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot.colorbar_object_id = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot.start_auto_play()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot.stop_auto_play()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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