Compact schemes for laser-matter interaction in Schrödinger equation

2018/05/23 by Arieh Iserles, Iserles, Arieh, Karolina Kropielnicka +3 · 1 citation
Mathematics · Physics and Astronomy · #65F60 (Secondary) #65L05 #65M70 (Primary) 35Q41 #Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Laser-Matter Interactions and Applications #Nonlinear Photonic Systems #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1805.09163

openalex publication_date 2018/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Numerical solutions for laser-matter interaction in Schrödinger 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 Schrödinger equation with time-indepedent potential to a fourth-order method for Schrödinger 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.

Citations

• On the exponential solution of differential equations for a linear operator

Cited by

• Uniform semiclassical observable error bound of Trotterization without the Egorov theorem: a simple algebraic proof

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