{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**soluzione dell'equazione di schrödinger**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "anche l'equazione di schrödinger è una ode: consideriamo l'equazione per il moto unidimensionale,\n",
    "\n",
    "$\\frac{\\hbar^2}{2m}\\frac{d^2}{dx^2}\\psi= (V-E)\\psi$\n",
    "\n",
    "possiamo facilmente riscriverla nella forma di una ode a due componenti:\n",
    "\n",
    "$y \\equiv [\\psi, \\psi'] \\equiv [r,s]$\n",
    "\n",
    "l'equazione di schrödinger, sarà allora:\n",
    "$y'=[\\psi', \\psi'']= [s, 2m/\\hbar^2(V-E) r]$\n",
    "\n",
    "per comodità lavoreremo in unità atomiche, dove $\\hbar=1$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "autoscroll": false,
    "collapsed": false,
    "ein.hycell": false,
    "ein.tags": "worksheet-0",
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f91df17f050>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.integrate as ntg\n",
    "\n",
    "def potential(x, a, d):\n",
    "    if x<-a:\n",
    "        return 0.0\n",
    "    elif x>a:\n",
    "        return 0.0\n",
    "    else:\n",
    "        return d*np.sqrt(a**2-x**2)\n",
    "\n",
    "vpotential=np.vectorize(potential)\n",
    "\n",
    "x=np.linspace(-5.0, 5.0, 101)\n",
    "y=vpotential(x,2.0, 10.0)\n",
    "plt.plot(x,y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "la funzione np.vectorize ci permette di prendere una qualunque funzione puntuale definita da noi e\n",
    "trasformarla in una funzione che opera su array\n",
    "\n",
    "abbiamo definito un potenziale a forma di muro, adesso\n",
    "\n",
    "a. scrivete una funzione che soddisfi l'equazione di schrödinger come l'abbiamo scritta sopra, dovrà\n",
    "accettare come parametri la massa m, una funzione potenziale v, e restituire $y'$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def schr(x, y, m, v, E):\n",
    "    psi,psid=y\n",
    "    psidd=(v(x)-E)*psi/2/m\n",
    "    return [psid, psidd]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "b. impostate le condizioni iniziali per il problema, una particella uscente da destra, pertanto\n",
    "rispondente alla forma $\\psi=e^{-ikx}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def iniziale(k):\n",
    "    return [complex(1), complex(0, -k)]   # "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1j, (-2.5+0j)]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#prova schr\n",
    "schr(-5, iniziale(1), 1, lambda xx:potential(xx,2,10), 5.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "c. risolvete l'equazione differenziale nell'intervallo definito dalla x nel riquadro precedente e nel\n",
    "grafico"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import ode\n",
    "import math\n",
    "co=ode(schr).set_integrator('zvode', method='bdf')   # integratore adatto anche per numeri complessi\n",
    "massa=1.0\n",
    "energia=15.0\n",
    "k=math.sqrt(energia*2*massa)\n",
    "psiv_in=iniziale(k)\n",
    "co.set_initial_value(psiv_in, -5).set_f_params(massa, lambda xx: potential(xx, 2.0, 10.0), energia)\n",
    "psiv=[psiv_in]+[co.integrate(xi) for xi in x[1:]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/fc/.local/python3.11/lib/python3.11/site-packages/matplotlib/cbook/__init__.py:1335: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f91dfa97910>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,(ax1,ax2)=plt.subplots(nrows=2, sharex=True)\n",
    "ax1.plot(x,y)\n",
    "psi_v=[p[0] for p in psiv]\n",
    "psi_d=[p[1] for p in psiv]\n",
    "ax2.plot(x,psi_v, label='$\\psi$')\n",
    "ax2.plot(x,psi_d, label=\"$\\psi'$\")\n",
    "ax2.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": "worksheet-0",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "d. ottenete i coefficienti di trasmissione e di riflessione, ovvero le componenti di $e^{ikx}$ e\n",
    "$e^{-ikx}$ nella soluzione finale,\n",
    "\n",
    "eseguite ciascuno di questi passaggi in una cella diversa aiutandovi nell'analisi con dei grafici."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align} \n",
    "\\psi &=&a e^{ikx}+b e^{-ikx}\\\\\n",
    "\\psi' &=&ik(a e^{ikx}-b e^{-ikx})\n",
    "\\end{align}\n",
    "\n",
    "\\begin{align}\n",
    "ik \\psi + \\psi' &=& 2ika\\\\\n",
    "ik \\psi - \\psi' &=& 2ikb\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((-0.00016970129196069934-38.49728035442339j),\n",
       " (35.67716445002244-14.497601655103741j))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psi_in=psiv[-1][0]\n",
    "psi_in_d=psiv[-1][1]\n",
    "a=(psi_in_d+complex(0,k)*psi_in)/complex(0,2*k)\n",
    "b=(-psi_in_d+complex(0,k)*psi_in)/complex(0,2*k)\n",
    "a,b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0017917544790857648"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trasmissione=1/np.vdot(a,b).real\n",
    "riflessione=1-trasmissione\n",
    "trasmissione"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def calcola_trasmissione(E):\n",
    "    co=ode(schr).set_integrator('zvode', method='bdf')   # integratore adatto anche per numeri complessi\n",
    "    massa=1.0\n",
    "    energia=E\n",
    "    k=math.sqrt(energia*2*massa)\n",
    "    psiv_in=iniziale(k)\n",
    "    co.set_initial_value(psiv_in, -5).set_f_params(massa, lambda xx: potential(xx, 2.0, 10.0), energia)\n",
    "    psiv=[psiv_in]+[co.integrate(xi) for xi in x[1:]]\n",
    "    psi_in=psiv[-1][0]\n",
    "    psi_in_d=psiv[-1][1]\n",
    "    a=(psi_in_d+complex(0,k)*psi_in)/complex(0,2*k)\n",
    "    b=(-psi_in_d+complex(0,k)*psi_in)/complex(0,2*k)\n",
    "    trasmissione=abs(1/np.vdot(a,b).real)\n",
    "    return trasmissione"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "Ev=np.arange(10,19,0.05)\n",
    "trv=[calcola_trasmissione(Ei) for Ei in Ev]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f91dc9a4dd0>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Ev, trv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.161088700855337e-06,\n",
       " 1.2339087476661656e-06,\n",
       " 1.3138190711763479e-06,\n",
       " 1.4017269678393598e-06,\n",
       " 1.4984780368587829e-06,\n",
       " 1.60504406123166e-06,\n",
       " 1.7226622524891479e-06,\n",
       " 1.852751916004122e-06,\n",
       " 1.9966337387820357e-06,\n",
       " 2.156319047301669e-06,\n",
       " 2.3336037130666346e-06,\n",
       " 2.5310604755779235e-06,\n",
       " 2.7511897669846677e-06,\n",
       " 2.9972385773716416e-06,\n",
       " 3.2729423163697386e-06,\n",
       " 3.582230827424936e-06,\n",
       " 3.929240114945694e-06,\n",
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     "execution_count": 20,
     "metadata": {},
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   "source": [
    "trv\n",
    "\n"
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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