{ "cells": [ { "cell_type": "markdown", "id": "63636091", "metadata": {}, "source": [ "# Equation de Schrödinger et états comprimés\n", "\n", "Ce TD a pour but de simuler numériquement le TD \"Etats quantiques d’atomes de césium dans un piège harmonique\" du cours de physique quantique.\n", "\n", "On prendra $m=1$, $\\hbar=1$. On considère de plus un piège harmonique de pulsation $\\omega = 2\\pi$. \n", "\n", "1. Ecrire (avec un papier et un crayon!) l'équation de Schrödinger. \n", "\n", "2. Ecrire (avec un papier et un crayon) la fonction d'onde de l'état fondamental du piège harmonique. \n", "\n", "On va échantillonner l'espace entre -5 et 5 avec un pas de 0.02\n", "\n", "3. Ecrire une fonction Python qui calcule un état Gaussien d'écart type $\\sigma_x$ de vitesse $v_0$ et centré en $x_0$. \n", "\n", "4. Ecrire une fonction Python qui calcule le Laplacien d'une fonction d'onde $\\psi$.\n", "\n", "5. Ecrire la fonction Python `psi_prime(t, psi, V)` qui donne la dérivée de psi. Vérifier graphiquement que l'on a bien $\\frac{\\partial \\psi}{\\partial t} = -i\\frac{\\omega}{2} \\psi$ pour l'état fondamental du piège. \n", "\n", "6. Résoudre numériquement sur un temps $t=1.5$ l'équation de Schrödinger pour différents états initiaux : par exemple un paquet centré en $-2$ initialement au repos et de largeur $0.3$. On utilisera la méthode `RK23`.\n", "\n", "7. Ecrire une fonction python `moments_x(psi)` qui retourne $\\mathbb{E}(X)$ (position moyenne) et $\\mathbb{E}((X - \\mathbb{E}(X))^2)$ (carré de la largeur du paquet)\n", "\n", "8. Tracer ces moments en fonction de t.\n", "\n", "9. Question 7 et 8, mais avec l'impulsion. Dans le calcul de l'espérance, on suprimera les parties hautes impulsions qui sont dûes à du bruit numérique\n", "\n", "10. Pendant 0.5 seconde, on laisse la paquet évoluer librement (V=0) puis pendant une durée $t<0.5$, le paquet évolue avec le potentiel harmonique. Tracer la largeur en impulsion en fonction de cette durée. \n" ] }, { "cell_type": "markdown", "id": "501f2f54", "metadata": { "tags": [ "sol" ] }, "source": [ "--------------------------------------------------------------------------------------\n", "\n", "## Solution" ] }, { "cell_type": "markdown", "id": "01566c9f", "metadata": { "tags": [ "sol" ] }, "source": [ "Equation de Schrödinger : \n", "\\begin{equation}\n", "i\\hbar\\frac{\\partial\\psi}{\\partial t} = -\\frac{\\hbar^2}{2m}\\frac{\\partial^2\\psi}{\\partial x} + \\frac{1}{2} m \\omega^2 x^2\n", "\\end{equation}\n", "\n", "Etat fondamental : on définit $a_\\mathrm{oh} = \\sqrt{\\frac{\\hbar}{m\\omega}}$. L'état fondamental est donné par :\n", "\\begin{equation}\n", "\\psi_0 = \\frac{1}{\\left( \\pi a^2_\\mathrm{oh}\\right)^{\\frac{1}{4}}} e^{-\\frac{x^2}{2a_\\mathrm{oh}^2}}\n", "\\end{equation}\n", "\n", "a_ho = np.sqrt(hbar/(m*omega))\n", "psi_0 = gaussian_packet(a_ho, 0, 0)" ] }, { "cell_type": "code", "execution_count": 1, "id": "1829db03", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from matplotlib import animation\n", "from IPython.display import HTML\n", "\n", "import numpy as np\n", "from scipy import integrate\n", "\n", "from numba import jit, njit" ] }, { "cell_type": "code", "execution_count": 2, "id": "f43475d4", "metadata": {}, "outputs": [], "source": [ "#Question 3\n", "\n", "L = 10.\n", "dx = 0.02\n", "N_x = int(round(L/dx))\n", "\n", "x = (np.arange(N_x)-N_x//2)*dx\n", "\n", "\n", "m = 1\n", "hbar = 1\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "63caec1b", "metadata": {}, "outputs": [], "source": [ "\n", "def norm(psi):\n", " return np.sqrt(np.sum(dx*np.abs(psi)**2))\n", "\n", "\n", "def gaussian_packet(sigma, x_0=0, v_0=0):\n", " k_x = m*v_0/hbar\n", " psi = np.exp(-(x-x_0)**2 / (2.0 * sigma**2)) * np.exp(1j * k_x * x)\n", " psi = psi / norm(psi)\n", " return psi" ] }, { "cell_type": "code", "execution_count": 4, "id": "d8bd4c97", "metadata": {}, "outputs": [], "source": [ "T = 1\n", "omega = 2*np.pi / T\n", "\n", "V = 0.5 * m * omega**2 * x**2" ] }, { "cell_type": "code", "execution_count": 5, "id": "0d93814e", "metadata": {}, "outputs": [], "source": [ "# Question 4\n", "\n", "@jit\n", "def Laplace(psi, dx=dx):\n", " output = np.zeros_like(psi)\n", " for i in range(1, N_x-1):\n", " output[i] = (psi[i-1] + psi[i+1]) - 2*psi[i]\n", " output[0] = psi[1] - 2*psi[0]\n", " output[-1] = psi[-2] - 2*psi[-1]\n", " return output/(dx**2)" ] }, { "cell_type": "code", "execution_count": 6, "id": "6f604f08", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.78 µs ± 31.1 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n" ] } ], "source": [ "psi = gaussian_packet(1.5, 10)\n", "_ = Laplace(psi)\n", "\n", "%timeit Laplace(psi)" ] }, { "cell_type": "code", "execution_count": 7, "id": "ec26aff4", "metadata": {}, "outputs": [], "source": [ "# Question 5\n", "def psi_prime(t, psi, V):\n", " return -1j * (- 0.5 * hbar / m * Laplace(psi) + V / hbar * psi)\n", "psi_prime(0.0, psi, V);" ] }, { "cell_type": "code", "execution_count": 8, "id": "686a490e", "metadata": {}, "outputs": [], "source": [ "#%timeit psi_prime(0.0, psi)" ] }, { "cell_type": "code", "execution_count": 9, "id": "1947a582", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$|\\\\psi|^2$')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# On vérifie que l'on a bien un état propre\n", "\n", "a_ho = np.sqrt(hbar/(m*omega))\n", "psi_0 = gaussian_packet(a_ho, 0, 0)\n", "\n", "plt.plot(x, np.abs(-1J*omega/2*psi_0)**2)\n", "plt.plot(x, np.abs(psi_prime(0, psi_0, V))**2)\n", "plt.xlabel('x')\n", "plt.ylabel(r'$|\\psi|^2$')" ] }, { "cell_type": "code", "execution_count": 10, "id": "62317072", "metadata": {}, "outputs": [], "source": [ "# Question 6\n", "\n", "t0 = 0.0\n", "tf = 1.5\n", "t_eval = np.linspace(t0, tf, 101)\n", "\n", "psi_0 = gaussian_packet(.3, -2, 0)\n", "\n", "sol = integrate.solve_ivp(psi_prime, t_span = [t0, tf], y0 = psi_0, t_eval = t_eval, method=\"RK23\", args=(V,))" ] }, { "cell_type": "code", "execution_count": 11, "id": "4875fd78", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x, np.abs(psi_0)**2)\n", "plt.plot(x, np.abs(sol.y[:, ::5])**2);\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "25b1456b", "metadata": {}, "outputs": [], "source": [ "# Question 7\n", "def moments_x(psi):\n", " proba = np.abs(psi)**2\n", " norm = np.sum(proba)\n", " center = np.sum(proba*x)/norm\n", " var = np.sum(proba*(x-center)**2)/norm\n", " return center, var\n", "\n", "centers, width = np.array([moments_x(psi) for psi in sol.y.T]).T" ] }, { "cell_type": "code", "execution_count": 13, "id": "ea795e75", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 't')" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Question 8\n", "fig = plt.figure()\n", "\n", "ax1, ax2 = fig.subplots(2, 1, sharex=True)\n", "\n", "ax1.plot(t_eval, centers)\n", "ax2.plot(t_eval, width)\n", "\n", "ax2.set_ylabel('Width')\n", "ax1.set_ylabel('Position')\n", "ax2.set_xlabel('t')" ] }, { "cell_type": "code", "execution_count": 14, "id": "a5ae3be5", "metadata": {}, "outputs": [], "source": [ "# Question 9\n", "\n", "p = np.fft.fftshift(hbar*2*np.pi*np.fft.fftfreq(len(x), d=dx))\n", "\n", "def psi_tilde(psi):\n", " out = np.fft.fftshift(np.fft.fft(psi))\n", " return out\n", "\n", "\n", "def moments_p(psi):\n", " mask = np.abs(p)<40\n", " proba = np.abs(psi_tilde(psi))**2\n", " norm = np.sum(proba[mask])\n", " center = np.sum(proba[mask]*p[mask])/norm\n", " var = np.sum(proba[mask]*(p[mask]-center)**2)/norm\n", " return center, var\n", "\n", "momentum, temperature = np.array([moments_p(psi) for psi in sol.y.T]).T" ] }, { "cell_type": "code", "execution_count": 15, "id": "fabc9753", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 't')" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "\n", "ax1, ax2 = fig.subplots(2, 1, sharex=True)\n", "\n", "ax1.plot(t_eval, momentum)\n", "ax2.plot(t_eval, temperature)\n", "\n", "ax1.set_ylabel('momentum')\n", "ax2.set_ylabel('temperature')\n", "ax2.set_xlabel('t')" ] }, { "cell_type": "code", "execution_count": 65, "id": "e92bfa89", "metadata": {}, "outputs": [], "source": [ "# Question 10\n", "\n", "t0 = 0.0\n", "tf = .5\n", "t_eval = np.linspace(t0, tf, 101)\n", "\n", "a_ho = np.sqrt(hbar/(m*omega))\n", "psi_0 = gaussian_packet(a_ho, 0, 0)\n", "\n", "sol = integrate.solve_ivp(psi_prime, t_span = [t0, tf], y0 = psi_0, \n", " t_eval = t_eval, method=\"RK23\", args=(0*V,))\n", "\n", "psi_1 = sol.y[:,-1]\n", "\n", "sol2 = integrate.solve_ivp(psi_prime, t_span = [t0, tf], y0 = psi_1, \n", " t_eval = t_eval, method=\"RK23\", args=(V,))\n" ] }, { "cell_type": "code", "execution_count": 66, "id": "e332d037", "metadata": {}, "outputs": [], "source": [ "momentum, temperature = np.array([moments_p(psi) for psi in sol2.y.T]).T" ] }, { "cell_type": "code", "execution_count": 68, "id": "471c1c7d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "\n", "ax = fig.subplots(1, 1, sharex=True)\n", "\n", "ax.plot(t_eval, np.sqrt(temperature))\n", "\n", "ax.set_ylabel(r'$\\Delta p$')\n", "ax.set_xlabel('t')\n", "ax.set_ylim(0, None)\n", "ax.set_xlim(0, None)\n", "ax.grid()" ] }, { "cell_type": "code", "execution_count": null, "id": "8073f3b8", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "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": "3.8.8" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 5 }