Pseudospectral discretization of the time-dependent Schr\"odinger equation

TL;DR

This paper discusses the application of pseudospectral methods to discretize and solve the time-dependent Schrödinger equation for single-particle systems interacting with classical electromagnetic fields, focusing on spherical coordinates.

Contribution

It introduces a pseudospectral discretization approach for the Schrödinger equation in spherical coordinates, detailing implementation for time-dependent problems.

Findings

Effective discretization of Schrödinger equation using pseudospectral methods.

Implementation details for single-particle systems in electromagnetic fields.

Potential for improved numerical accuracy in quantum simulations.

Abstract

The purpose of this document is to describe the solution and implementation of the time-independent and time-dependent Schr\"odinger using pseudospectral methods. Currently, the description is for single particle systems interacting with a classical electromagnetic field in spherical coordinates.