New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation

A propagation method for the time dependent Schrödinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde’s usually results in system of ode’s of the form 0.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_t - G u =s$$\end{document} where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorithm for the more general case where s is a time-dependent r.h.s vector. An iterative version of the new algorithm can be applied to the general case where G depends on t or u. Numerical results for Schrödinger equation with time-dependent potential and to non-linear Schrödinger equation will be presented.

• Publication year

  2012

• Venue

  Journal of Scientific Computing

• Publication date

  2012-03-07

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1007/s10915-012-9583-xarXiv 1204.3766
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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