A short note on simplified pseudospectral methods for computing ground state and dynamics of spherically symmetric Schrodinger--Poisson--Slater system

TL;DR

This paper simplifies pseudospectral methods for efficiently computing the ground state and dynamics of spherically symmetric Schrödinger--Poisson--Slater systems by reducing the problem to a quasi-1D model, lowering computational costs.

Contribution

It introduces a simplified pseudospectral approach tailored for spherically symmetric SPS systems, significantly reducing computational and memory requirements.

Findings

Methods are more efficient for spherical symmetry cases.

Significant reduction in computational load.

Maintains accuracy of the original methods.

Abstract

In a recent paper we proposed and compared various approaches to compute the ground state and dynamics of the Schr\"{o}dinger--Poisson--Slater (SPS) system for general external potential and initial condition, concluding that the methods based on sine pseudospectral discretization in space are the best candidates. This note is concerned with the case that the external potential and initial condition are spherically symmetric. For the SPS system with spherical symmetry, via applying a proper change of variables into the reduced quasi-1D model we simplify the methods proposed for the general 3D case such that both the memory and computational load are significantly reduced.