Squeezed Quantum States in Two Dimensions

Live Script exploring numerical integration of the time-dependent Schrödinger equation in two dimensions with squeezed coherent states.

This educational Live Script explores time-dependent solutions to the Schrödinger equation in two dimensions using a second-order, fourth-order, or sixth-order stencil in space, sparse matrices, and ode45 adaptive integration in time and alternatively matrix exponential time integration. Numerical results for the evolution of Gaussian wave packets called squeezed coherent states in a two-dimensional anisotropic harmonic oscillator potential are compared to analytic results. A quartic term in the potential may be added to disrupt the wave functions.

This script may interest students and instructors in physics and related fields. 'Try this" suggestions, 'Challenges,' hyperlinks, and references are provided for further exploration. Additional related Live Scripts by the author are available here.