A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation
type: Item
instance of: scholarly article
title: A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation
zbMATH Open document ID: 0941.65080
DOI: 10.1016/S0010-4655(99)00224-6
author: I. V. Puzynin
author: Alexei V. Selin
author: S. I. Vinitsky
published in: Computer Physics Communications
publication date: 2000-07-20T00:00:00Z
review text: The paper presents the implicit difference \(O(\tau^{2m})\)-schemes in terms of the Magnus expansion for the evolution operator of the time-dependent Schrödinger equation and its further factorization with the help of diagonal Padé approximations. These schemes can be viewed as generalization of the well-known Crank-Nicolson algorithm. The efficiency of the method is illustrated by numerical experiments for the oscillator with time-dependent frequency.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 1394619
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: Magnus expansion
zbMATH Keywords: Padé approximation
zbMATH Keywords: Crank-Nicolson algorithm
zbMATH Keywords: implicit difference schemes
zbMATH Keywords: numerical experiments
zbMATH Keywords: oscillator
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
full work available at URL: s0010-4655(99)00224-6
OpenAlex ID: W2068994783
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description: scientific article; zbMATH DE number 1394619