Quantum Mechanics in 2D with the PDE Toolbox

Computes 2-dimensional quantum eigenstates for arbitrary geometries and potentials.

This educational Live Script shows how to solve the Schrodinger equation numerically for the eigenmodes and eigenfrequencies of a quantum particle bound by any two-dimensional model potential with essentially any two-dimensional geometry using the Partial Differential Equation Toolbox®. Example potential models are combinations of a 2D harmonic oscillator and a uniform constant force field. Example geometries include rectangles and circles with or without holes and multiple overlapping circular regions.

This script may interest students and instructors of physics, chemistry, and related fields. 'Try this' suggestions, 'Challenges', hyperlinks, and references are provided for further exploration. Related Live Scripts quantum physics education by the author are available (Ref[1-5]) and additional physics and general STEM Live Scripts at the File Exchange.