{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "87940e76", "metadata": {}, "source": [ "# Diagonalizing a Hamiltonian (PDE eigenvalue problems)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "8da43b3d", "metadata": {}, "source": [ "## Solving the Schrodinger Equation for a 2d Harmonic oscillator" ] }, { "attachments": {}, "cell_type": "markdown", "id": "8080c079", "metadata": {}, "source": [ "In this example, we will show how to use the CoLA library to solve for the eigenvalues and eigenfunctions of the Hamiltonian operator for a two-dimensional quantum harmonic oscillator. The Hamiltonian operator is defined as\n", "\n", "H = -Δ/2 + V(x)\n", "\n", "where Δ is the Laplacian operator and V(x) is the potential energy function. We will be using a discretized Laplacian on a square grid and a simple harmonic potential V(x) = x²/2.\n", "\n", "To start, let's create a 1000 x 1000 point coordinate mesh:" ] }, { "cell_type": "code", "execution_count": 1, "id": "001cbe0d", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING:jax._src.xla_bridge:CUDA backend failed to initialize: Found CUDA version 12000, but JAX was built against version 12020, which is newer. The copy of CUDA that is installed must be at least as new as the version against which JAX was built. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n" ] } ], "source": [ "import numpy as np\n", "import jax.numpy as jnp\n", "from jax import vmap, jit\n", "import jax\n", "import cola\n", "from jax.config import config; config.update(\"jax_enable_x64\", False)\n", "jax.config.update('jax_platform_name', 'cpu')\n", "\n", "N = 300\n", "ndims = 2\n", "grid = jnp.linspace(-30,30,N)\n", "dx = grid[1]-grid[0]\n", "xyz = jnp.stack(jnp.meshgrid(*(ndims * [grid])), axis=-1).reshape(-1, ndims)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "93087dcb", "metadata": {}, "source": [ "Here, N is the number of points in each dimension, ndims is the number of dimensions, and grid represents the grid points from -30 to 30. dx represents the grid spacing, and xyz is an array of 2D points representing the coordinates of each point in the grid.\n", "\n", "Next, we define the Laplacian operator. We use the same finite difference stencil as in the previous example to discretize the Laplacian." ] }, { "cell_type": "code", "execution_count": 2, "id": "53d9854c", "metadata": {}, "outputs": [], "source": [ "def laplacian(x):\n", " x = x.reshape(ndims*(N,)) # unflatten to an ndims-dimensional grid\n", " cderiv = lambda x: jax.scipy.signal.correlate(x,jnp.array([1.,-2,1.])/dx**2,mode='same')\n", " return sum([jnp.apply_along_axis(cderiv,i,x) for i in range(ndims)]).reshape(-1)\n", "\n", "L = cola.ops.LinearOperator(jnp.float32, shape=(N**ndims, N**ndims), matmat=jit(vmap(laplacian, -1, -1)))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "f8ab1e45", "metadata": {}, "source": [ "The function laplacian calculates the second derivative along each dimension and sums them up. The result is reshaped to a 1D array and returned.\n", "\n", "Next, we define the potential function V(x) as a diagonal operator:" ] }, { "cell_type": "code", "execution_count": 3, "id": "e9e56f7c", "metadata": {}, "outputs": [], "source": [ "def vfn(x):\n", " return (x * x).sum() / 2\n", "\n", "V = cola.ops.Diagonal(vmap(vfn)(xyz).reshape(-1))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "6765c7f9", "metadata": {}, "source": [ "vfn calculates the potential energy for a given point in the grid. cola.diag creates a diagonal operator with the calculated potential energy values on the diagonal. vmap is a function from the JAX library that applies the function vfn to each point in xyz.\n", "\n", "Next, we define the Hamiltonian operator and compute its eigenvalues and eigenvectors:" ] }, { "cell_type": "code", "execution_count": 8, "id": "2b696c83", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING:root:Non keyed randn used. To be deprecated soon.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "5dde411b0bc14f10bea3b2ac0d886af0", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Running body_fun: 0%| | 0/100 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nm = np.stack(np.meshgrid(np.arange(10),np.arange(10)), axis=-1).reshape(-1, 2)\n", "Enm = 1+nm[:,0]+nm[:,1]\n", "nm = nm[Enm.argsort()]\n", "Enm = np.sort(Enm)\n", "\n", "import matplotlib.pyplot as plt\n", "fig, axs = plt.subplots(1, figsize=(5, 3))\n", "axs.plot(energy_levels[:25], 'o',alpha=0.5, label=\"Numerical\")\n", "axs.plot(Enm[:25], 'o', color='k',alpha=0.5, label=\"Analytical\")\n", "plt.legend()\n", "plt.xlabel(\"index\")\n", "plt.ylabel(\"Energy Level\")\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "696d5a6a", "metadata": {}, "source": [ "Each point represents an eigenvalue, which corresponds to an energy level of the quantum harmonic oscillator. Up to errors produced by the finite boundary (at [-30,30]) and discretization, we see the familiar $E_{nm} = (1/2+n)+(1/2+m)$ energy levels for the 2d oscillator.\n", "\n", "Lastly, we visualize the corresponding eigenfunctions:" ] }, { "cell_type": "code", "execution_count": 10, "id": "0c74eeef", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "fig, axs = plt.subplots(2, 4, figsize=(8, 4))\n", "for i,ax in enumerate(axs.flatten()):\n", " l = 30\n", " ax.imshow(eigenfunctions[:, i].reshape(N,N)[N//2-l:N//2+l,N//2-l:N//2+l],\n", " extent=[grid[N//2-l],grid[N//2+l],grid[N//2+l],grid[N//2-l]],\n", " cmap='RdBu_r', vmin=-0.1, vmax=0.1)\n", " ax.set_title(r\"$E_{{{}}} ={:.3f}$\".format(\"n,m\",energy_levels[i]))\n", " ax.axis('off')" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7a2c2e7f", "metadata": {}, "source": [ "Each subplot represents an eigenfunction, reshaped to 2D and displayed as an image. The eigenfunctions correspond to the wave functions of the quantum harmonic oscillator at different energy levels. The color represents the value of the wave function at each point in the grid. The title of each subplot shows the corresponding eigenvalue, or energy level.\n", "\n", "Through this example, we have shown how to solve for the energy levels and wave functions of a quantum harmonic oscillator using the CoLA library." ] }, { "attachments": {}, "cell_type": "markdown", "id": "c0195343", "metadata": {}, "source": [ "## 🚧 Solving Schrodinger for the Hydrogen atom in 3d 🚧" ] }, { "cell_type": "markdown", "id": "f569bc2d", "metadata": {}, "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 5 }