Quantum Mechanics in 1D with the PDE Toolbox

Live script exploring eigenstates of the Schrodinger equation in one dimension with the PDE Toolbox.

This Live Script explores bound stationary-state solutions to the one-dimensional Schrodinger equation using the Partial Differential Equation (PDE) Toolbox®. Illustrative problems solved are 1) a particle in an infinite square well, 2) a particle in an infinite square well subject to a uniform force field creating a triangular well, 3) a particle in a finite square well within an infinite square well, 3) a particle subject to a harmonic oscillator potential within an infinite square well. Analytic solutions for the first two cases are used to assess the accuracy of the numerical method and to guide the understanding of the other two cases. Direct finite difference methods of solution are explored in Ref[1-2]. The Partial Differential Toolbox offers an alternate convenient way to solve such problems.

This script may interest students and instructors in physics and related fields. 'Try this' suggestions, challenges, hyperlinks, and references are included for further exploration. For additional educational Live Scripts by the author touching quantum physics and other topics, see the File Exchange.