Solving the Schrodinger Equation for a Charged Particle in a Magnetic Field using the Finite Difference Time Domain Method

TL;DR

This paper extends the finite difference time domain method to solve the Schrödinger equation with complex eigenfunctions, demonstrating its accuracy through numerical simulations of an electron in a magnetic field.

Contribution

It introduces an extension of the FDTD method for complex eigenfunctions in Schrödinger equation simulations, applicable to magnetic field problems.

Findings

Accurate numerical solutions for an electron in a magnetic field.

Validation of the extended FDTD method against known results.

Demonstrated effectiveness in two-dimensional quantum systems.

Abstract

We extend our finite difference time domain method for numerical solution of the Schrodinger equation to cases where eigenfunctions are complex-valued. Illustrative numerical results for an electron in two dimensions, subject to a confining potential V(x,y), in a constant perpendicular magnetic field demonstrate the accuracy of the method.