{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# **Numerical Solution of the Schrödinger Equation for a One Dimensional Quantum Well**\n", "\n", "**Authors:** Dou Du, Taylor James Baird and Giovanni Pizzi\n", "\n", " Go back to index\n", "\n", "**Source code:** https://github.com/osscar-org/quantum-mechanics/blob/master/notebook/quantum-mechanics/1quantumwell.ipynb\n", "\n", "This notebook solves numerically the quantum-mechanical problem of a single rectangular one-dimensional quantum well, and displays interactively the eigenfunctions (plotted at the height of the corresponding eigenvalues).\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Goals**\n", "* Investigate quantum confinement by manipulating the depth and width of a finite one-dimensional quantum well.\n", "* Learn how to solve the Schrödinger equation by matrix diagonalization.\n", "* Understand quantum tunnelling in regions where the energy is lower than the potential." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Background theory** \n", "\n", "[More on the background theory.](./theory/theory_1quantumwell.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Tasks and exercises**\n", "\n", "1. Keep the depth at the default value (-0.2) and move the slider of the width from the\n", "smallest value (0.1) to the largest value (2.0). Do you see any change for the number\n", "of the states? How does the eigenvalue of the ground state (the lowest eigenstate) change \n", "with the increasing of the width of the quantum well and why?\n", "\n", "
\n", " Solution\n", " The wider the well potential is, the more (bound state) wavefunctions you will obtain. The reason for this can be traced back to the relationship between the eigenenergies of the bound states and the width of the well: $E_n \\propto \\frac{1}{L^2}$. Therefore, increasing the width of the well decreases the values of the various eigenergies. A different explanation for the decreased energy of the bound states with increasing well width can be found by appealing to Heisenberg's uncertainty principle: the less confined a particle is (and thus the less certain we are of its position), the more certain we are of its momentum. This smaller spread in momentum values translates into smaller values for the particle's kinetic energy. In addition, there are consequently more states which satisfy $ E_n < V$ (where $V$ is the well depth) and this leads to an increase in the number of bound states. \n", " Note that the \"zero\" of the wavefunction is shifted, for every wavefunction, at the energy of the corresponding eigenvalue.\n", "
\n", " \n", "2. Keep the width at the default value (1.2) and move the slider of the depth from\n", "the smallest value (-1.0) to the largest value (0.0). Do you see any change for the \n", "number of the states? How does the eigenvalue of the ground state (the lowest eigenstate)\n", "change with the increasing of the depth of the quantum well and why?\n", "\n", "
\n", " Solution\n", " The deeper the well potential is, the more wavefunctions you will obtain. Mathematically, the explanation for this lies in the relationship between the values of the eigenergies and the potential depth. This is a transcendental relationship and has to be solved numerically or graphically but one may note that by increasing the well depth, the values of the various energy eigenvalues are increased.Some important remarks are that, regardless of the well depth, there is always at least one bound solution in one dimension and that as the depth is made progressively larger, the energy levels shall approach those of the infinite square well. For more information see \n", " Wikipedia.\n", " Note that the \"zero\" of the wavefunction is shifted, for every wavefunction, \n", " at the energy of the corresponding eigenvalue.\n", "
\n", "\n", "3. Investigate the role played by quantum confinement in this 1D potential well system by varying the width of the well via the \"width\" slider and observing the spacing of the energy levels of the system.\n", "\n", "
\n", " Solution\n", " \n", " When the dimension of the confining potential becomes comparable to the de Broglie wavelength of the confined particle then we begin to observe so-called confinement effects. These manifest as a discretization of the bound state energy levels (when the de Broglie wavelength and well width are not comparable the particle behaves essentially like a free particle, with a continuous energy spectrum). As mentioned in task 1, the relationship between the energy levels and the width of the well is $E_n \\propto \\frac{1}{L^2}$; consequently, as we decrease the width of the well, the spacing of the energy levels becomes larger and larger. As an application of this effect we note that in a nanostructure the effect of increased confinement (reducing the size of the structure) is to increase the band gap of that structure. This can be leveraged to manipulate the opto-electronic properties of the nanostructure. \n", " Furthermore, we note that in a classical potential, the lowest energy state would be at the bottom of the well. In quantum mechanics, the lowest energy state has a higher energy \n", " than the bottom of the quantum well, as you can see in the figure below. \n", " The reason for this energy difference is what is typically called the quantum \n", " confinement effect. Observe also how the lowest energy state changes with \n", " the width of the well potential. \n", "
\n", " \n", "4. Keeping the sliders for the width and the height of the well at their default values and selecting the \"Probability density\" option, investigate the probability of a previously confined particle tunnelling through the potential well.\n", "\n", "
\n", " Solution\n", " One can see that even although the potential outside the well is greater than the energy of the particle, there exists a non-zero probability of finding said particle at a position outside the well. This possibility of the particle \"tunnelling\" through the potential barrier in this way is a purely quantum mechanical effect. In the classical picture of this system one would never expect to observe the particle outside the confines of the potential well. \n", "
\n", " \n", "5. Please read the background theory section and try to understand the core of the\n", "numerical algorithm. Why is the diagonalization of the Hamiltonian matrix key to \n", "solve the Schrödinger equation?\n", "\n", "
\n", " Solution\n", " As shown in the background theory section, the Schrödinger equation is an \n", " eigenvalue equation. In mathematics, diagonalization of the matrix allows us\n", " to obtain its eigenvalues and eigenfunctions. You can read more \n", " about the theory on \n", " Wikipedia.\n", "
\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Interactive visualization**\n", "(be patient, it might take a few seconds to load)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib widget\n", "\n", "from numpy import linspace, sqrt, ones, arange, diag, argsort, zeros\n", "from scipy.linalg import eigh_tridiagonal\n", "import matplotlib.pyplot as plt\n", "from ipywidgets import FloatSlider, jslink, VBox, HBox, Button, Label, RadioButtons" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "colors = ['#a6cee3','#1f78b4','#b2df8a','#33a02c','#fb9a99','#e31a1c','#fdbf6f','#ff7f00','#cab2d6','#6a3d9a','#ffff99','#b15928']\n", "ixx = 0\n", "\n", "def singlewell_potential(x, width, depth):\n", " x1 = zeros(len(x))\n", " for i in range(len(x)):\n", " if x[i] > - width/2.0 and x[i] < width/2.0:\n", " x1[i] = depth\n", " return x1\n", " \n", "\n", "def diagonalization(hbar, L, N, pot=singlewell_potential, width = 0.1, depth = 0.0):\n", " \"\"\"Calculate sorted eigenvalues and eigenfunctions by diagonalization of the Hamiltonian matrix. \n", "\n", " Input:\n", " hbar: reduced Planck constant\n", " L: set discretized interval as [-L,L] \n", " N: number of grid points, i.e., size of the H matrix \n", " pot: python function returning the value of the potential energy\n", " x0: center of the quantum well\n", " width: the width of the quantum well\n", " depth: the depth of the quantum well\n", " Ouput:\n", " ew: sorted eigenvalues (array of length N)\n", " ef: sorted eigenfunctions, ef[:,i] (size N*N)\n", " x: grid points (array of length N)\n", " dx: grid spacing (called Delta in the theory above)\n", " V: values of the potential discretized on the grid x (array of length N)\n", " \"\"\"\n", " x = linspace(-L, L, N+2)[1:N+1] # grid points\n", " dx = x[1] - x[0] # grid spacing\n", " V = pot(x, width, depth)\n", " z = hbar**2 /2.0/dx**2 # coefficient\n", "\n", " ew, ef = eigh_tridiagonal(V+2.0*z, -z*ones(N-1))\n", " ew = ew.real # real part of the eigenvalues\n", " ind = argsort(ew) # Indices f. sort. Array\n", " ew = ew[ind] # Sort the ew by ind\n", " ef = ef[:, ind] # Sort the columns \n", " ef = ef/sqrt(dx) # Correct standardization \n", " return ew, ef, x, dx, V\n", "\n", "\n", "def plot_eigenfunctions(ax, ew, ef, x, V, width=1, Emax=0.05, fak= 5.0):\n", " \"\"\"Create the full plot.\n", " \n", " Plot the lowest squared eigenfunctions 'ef' at the level of the eigenvalues\n", " 'ew' in the plot area 'ax', and the potential 'V(x)'.\n", " \"\"\"\n", " if psi_x.value == \"Wavefunction\":\n", " fig.suptitle('Numerical Solution ($\\psi$) of One Dimension Schrödinger Equation', fontsize = 13)\n", " else:\n", " fig.suptitle('Numerical Solution ($\\psi^2$) of One Dimension Schrödinger Equation', fontsize = 13)\n", " \n", " fak = fak/100.0\n", " \n", " ax[0].axhspan(0.0, Emax, facecolor='lightgrey')\n", " \n", " ax[0].set_xlim([min(x), max(x)])\n", " ax[0].set_ylim([min(V)-0.05, Emax])\n", " \n", " ax[0].set_xlabel(r'$x/a$', fontsize = 10)\n", " ax[0].set_ylabel(r'$V(x)$ and squared eigenfunctions', fontsize = 10)\n", " \n", " ax[1].set_xlim([min(x), max(x)])\n", " ax[1].set_ylim([min(V)-0.05, Emax])\n", " \n", " ax[1].yaxis.set_label_position(\"right\")\n", " ax[1].yaxis.tick_right()\n", " \n", " ax[1].get_xaxis().set_visible(False)\n", " ax[1].set_ylabel(r'$\\rm{\\ Eigenvalues}$', fontsize = 10)\n", " \n", " indmax = sum(ew<=0.0) \n", " if not hasattr(width, \"__iter__\"): \n", " width = width*ones(indmax) \n", " for i in arange(indmax): \n", " if psi_x.value == \"Wavefunction\":\n", " ax[0].plot(x, fak*(ef[:, i])+ew[i], linewidth=width[i]+.1, color=colors[i%len(colors)])\n", " else:\n", " ax[0].plot(x, fak*abs(ef[:, i])**2+ew[i], linewidth=width[i]+.1, color=colors[i%len(colors)])\n", "\n", " ax[1].plot(x, x*0.0+ew[i], linewidth=width[i]+2.5, color=colors[i%len(colors)])\n", " \n", " ax[0].plot(x, V, c='k', linewidth=1.6)\n", " " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "data": { 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", "text/html": [ "\n", "
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\n", " Figure\n", "
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\n", " " ], "text/plain": [ "Canvas(header_visible=False, layout=Layout(width='750px'), toolbar=Toolbar(toolitems=[('Home', 'Reset original…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "a42d094de1a64660826c79f20ee83769", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatSlider(value=1.2, description='Width: ', max=2.0, min=0.1), FloatSlider(value=-0.2, descri…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "aa92edcb72e44ebb93667a74f9b51176", "version_major": 2, "version_minor": 0 }, "text/plain": [ "FloatSlider(value=5.0, description='Zoom factor: ', max=10.0, min=1.0, step=1.0)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1a9ba3cd800d47f9a10b137c3f162c7a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(RadioButtons(description='Show:', options=('Wavefunction', 'Probability density'), value='Wavef…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu = 0.06 # Potential parameter\n", "L = 1.5 # x range [-L,L]\n", "N = 200 # Number of grid points\n", "hbar = 0.06 # Reduced Planck constant\n", "sigma_x = 0.1 # Width of the Gaussian function\n", "zeiten = linspace(0.0, 10.0, 400) # time\n", "\n", "\n", "swidth = FloatSlider(value = 1.2, min = 0.1, max = 2.0, description = 'Width: ')\n", "sdepth = FloatSlider(value = -0.2, min = -1.0, max = 0.0, step = 0.05, description = 'Depth: ')\n", "sfak = FloatSlider(value = 5, min = 1.0, max = 10.0, step = 1.0, description = r'Zoom factor: ')\n", "update = Button(description=\"Show all\")\n", "psi_x = RadioButtons(options=[\"Wavefunction\", \"Probability density\"], value=\"Wavefunction\", description=\"Show:\")\n", "\n", "width = 1.2\n", "depth = -0.2\n", "fak = 5.0\n", "\n", "ew, ef, x, dx, V = diagonalization(hbar, L, N, width = width, depth = depth)\n", " \n", "fig, ax = plt.subplots(1, 2, figsize=(7,5), gridspec_kw={'width_ratios': [10, 1]})\n", "fig.canvas.header_visible = False\n", "fig.canvas.layout.width = \"750px\"\n", "\n", "fig.suptitle(r'Numerical Solution ($\\psi^2$) of the Schrödinger Equation for a 1D Quantum Well', fontsize = 12)\n", "plot_eigenfunctions(ax, ew, ef, x, V)\n", "\n", "plt.show()\n", "\n", "def on_update_click(b):\n", " for i in ax[0].lines:\n", " i.set_alpha(1.0)\n", " for i in ax[1].lines:\n", " i.set_alpha(1.0)\n", " try:\n", " ann.remove()\n", " ann1.remove()\n", " except:\n", " pass\n", "\n", "def on_width_change(change):\n", " global ew, ef, x, dx, V\n", " ax[0].lines = []\n", " ax[1].lines = []\n", " \n", " try:\n", " ann.remove()\n", " ann1.remove()\n", " except:\n", " pass\n", "\n", " ew, ef, x, dx, V = diagonalization(hbar, L, N, width = swidth.value, depth = sdepth.value)\n", " plot_eigenfunctions(ax, ew, ef, x, V, fak = sfak.value)\n", "\n", "def on_depth_change(change):\n", " global ew, ef, x, dx, V\n", " ax[0].lines = []\n", " ax[1].lines = []\n", " \n", " try:\n", " ann.remove()\n", " ann1.remove()\n", " except:\n", " pass\n", "\n", " ew, ef, x, dx, V = diagonalization(hbar, L, N, width = swidth.value, depth = sdepth.value)\n", " plot_eigenfunctions(ax, ew, ef, x, V, fak = sfak.value)\n", " \n", "def on_xfak_change(change):\n", " ax[0].lines = []\n", " ax[1].lines = []\n", " \n", " try:\n", " ann.remove()\n", " ann1.remove()\n", " except:\n", " pass\n", "\n", " plot_eigenfunctions(ax, ew, ef, x, V, fak = sfak.value)\n", "\n", "def on_press(event):\n", " global ann, ann1, ixx\n", " \n", " ixx = min(enumerate(ew), key = lambda x: abs(x[1]-event.ydata))[0]\n", " \n", " for i in range(len(ax[1].lines)):\n", " ax[0].lines[i].set_alpha(0.1)\n", " ax[1].lines[i].set_alpha(0.1)\n", " ax[0].lines[i].set_linewidth(1.1)\n", " \n", " ax[0].lines[ixx].set_alpha(1.0)\n", " ax[1].lines[ixx].set_alpha(1.0)\n", " ax[0].lines[ixx].set_linewidth(2.0)\n", " \n", " try:\n", " ann.remove()\n", " ann1.remove()\n", " except:\n", " pass\n", " \n", " ann = ax[0].annotate(s = 'n = ' + str(ixx+1), xy = (0, ew[ixx]), xytext = (-0.15, ew[ixx]), xycoords = 'data', color='k', size=15)\n", " ann1 = ax[1].annotate(s = str(\"{:.3f}\".format(ew[ixx])), xy = (0, ew[ixx]), xytext = (-1.2, ew[ixx]+0.005), xycoords = 'data', color='k', size=9)\n", "\n", "cid = fig.canvas.mpl_connect('button_press_event', on_press)\n", "\n", "swidth.observe(on_width_change, names = 'value')\n", "sdepth.observe(on_depth_change, names = 'value')\n", "sfak.observe(on_xfak_change, names = 'value')\n", "update.on_click(on_update_click)\n", "psi_x.observe(on_width_change, names = 'value')\n", "\n", "label1 = Label(value=\"(click on a state to select it)\");\n", "\n", "display(HBox([swidth, sdepth]), sfak, HBox([psi_x, update, label1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* **Width:** the width of the quantum well.\n", "* **Depth:** the depth of the quantum well.\n", "* **Zoom factor:** the zoom factor for the magnitude of the eigenfunctions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "## **Legend**\n", "\n", "(How to use the interactive visualization)\n", "\n", "### Controls\n", "There are three sliders you can tune interactively. Two of them can adjust \n", "the width and depth of the potential well. The zoom factor slider is used \n", "to adjust the normalization factor of the wavefunctions. This factor is used for visualization \n", "purposes only, to avoid overlap of the wavefunctions whilst simultaneously preventing the wavefunctions from being so narrow that you cannot appreciate their shape.\n", "\n", "### Interactive figure\n", "In the main visualization part, there are two subplots. The wide figure on \n", "the left shows the well potential and the square moduli of the eigenfunctions \n", "$|\\psi|^2$ of different states, plotted at the energy of the corresponding \n", "eigenvalues. The narrow figure on the right shows the eigenvalues.\n", "You can select either an eigenfunction or an eigenvalue by clicking on \n", "it in one of the two subplots. The eigenfunction and corresponding eigenvalue \n", "will be highlighted, and the corresponding eigenenergy and value of the index \n", "$n$ will be shown. All other eigenstates will fade out. By clicking the \"Show all\" \n", "button, you can reset the plot and show all states again." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.12" }, "voila": { "authors": "Dou Du and Giovanni Pizzi" } }, "nbformat": 4, "nbformat_minor": 4 }