An open source virtual laboratory for the Schrödinger equation

Abstract

A simple Python-based open source software library for the numerical simulation of the linear or nonlinear time-dependent Schrödinger equation in one and two dimensions is presented. The integration is performed using a first-order split-step pseudospectral method, relying on the fast Fourier transform. The software library could be useful for undergraduate courses in elementary quantum mechanics, wave optics and computational physics. It could also be of interest for graduate students working with nonlinear waves, in frameworks such as laser beam propagation in nonlinear optical materials, matter waves within ultracold gases, dark matter or superfluid dynamics, among others. The discussion is complemented by solved examples and suggestions for educational applications of the code.

QMwebJS—An Open Source Software Tool to Visualize and Share Time-Evolving Three-Dimensional Wavefunctions

“…Throughout, we have argued that, mostly thanks to its accessibility, usage simplicity and adaptability, QMwebJS can be a useful resource to teach quantum mechanics courses, both for graphical demonstrations prepared by the teacher or as a useful application for student projects. In combination with a simulation module to integrate the 3D time-dependent Schrödinger equation (e.g., by adapting our previous contribution [28] to the 3D case), it may open many possibilities for inquiry-based learning of particular aspects of quantum mechanics. Certainly, it would be interesting to directly test, using physics education research methods, the influence of the utilisation of the software in improving the student understanding and motivation.…”

“…Both strategies would greatly benefit by combining QMwebJS with a simulation module to integrate the time-dependent 3D Schrödinger equation for a given potential and initial condition, in order to produce the input data to be visualized. In fact, we presented a Python-based tool of this sort in Reference [28] for the 1D and 2D cases, but it can be readily generalized to the 3D case (in fact, 3D was not included in Reference [28] mainly because of the difficulties in automatically producing attractive and informative 3D plots). In the Supplementary Materials (also see http://www.parvis3d.org.es/), we provide the code and simulation results of the examples shown below, that are 3D adaptation of the examples given in Reference [28].…”

A Simple and Ready to Use Code to Simulate Paraxial Beam Propagation

“…We have created a Python-based open source software library to integrate this equation in 1+1 or 1+2 dimensions [3]. The user can insert an initial condition, a potential and several inputs that define the numerical computation such as the number of points of the grid.…”

“…Taking this into account, we have developed a software library that provides a computational tool to students and young researchers dealing with laser beam propagation in non-trivial linear or nonlinear media. The present contribution is mostly based on our previous publication [3].…”

FisicaTIC, plataforma hardware-software para aplicaciones en física e ingeniería

“…PhET, es una plataforma de acceso libre, la cual es proporcionada por la universidad de Colorado de forma gratuita, cuenta con varias pruebas de laboratorio de física, biología, matemáticas y ciencias de la tierra entre otras [16], [17]. De otra parte, en la Universidad de Vigo España desarrollaron un laboratorio virtual de código abierto para la ecuación de Schrödinger, esta plataforma consiste en un software de código abierto basado en Python para la simulación numérica de la ecuación de Schrödinger lineal y no lineal en una y dos dimensiones [18]. En esta misma línea en la Universidad Tecnológica Nacional de Argentina, construyeron un volante Inercial usando un hardware, conformado por el volante, una pesa, una cuerda inextensible y un sensor de rotación, el cual adquiere los datos y los transmite en tiempo real a una computadora que contiene una aplicación para tal efecto [19].…”