Compact schemes for laser-matter interaction in Schr\"odinger equation

TL;DR

This paper introduces a cost-effective method to extend fourth-order numerical schemes for the Schrödinger equation to handle laser potentials, offering improved accuracy over many sixth-order schemes.

Contribution

The paper presents a novel methodology that adapts existing fourth-order schemes for Schrödinger equations to include laser potentials with minimal additional computational cost.

Findings

Enhanced fourth-order schemes for laser-matter interaction

Lower computational costs compared to sixth-order methods

Improved accuracy with small error constants

Abstract

Numerical solutions for laser-matter interaction in Schr\"odinger equation has many applications in theoretical chemistry, quantum physics and condensed matter physics. In this paper we introduce a methodology which allows, with a small cost, to extend any fourth-order scheme for Schr\"odinger equation with time-indepedent potential to a fourth-order method for Schr\"odinger equation with laser potential. These fourth-order methods improve upon many leading schemes of order six due to their low costs and small error constants.