Numerical L Methods for Schrödinger Equations

Weizhu Bao (), Shi Jin () and Peter A. Markowich ()
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Weizhu Bao: National University of Singapore, Department of Computational Science
Shi Jin: University of Wisconsin-Madison, Department of Mathematics
Peter A. Markowich: University of Vienna, Institute of Mathematics

A chapter in Recent Progress in Computational and Applied PDES, 2002, pp 27-38 from Springer

Abstract: Abstract In this note we review the time-splitting spectral method, recently studied by the authors, for linear[2] and nonlinear[3] Schrödinger equations (NLS) in the semiclassical regimes, where the Planck constant ɛ is small. The time-splitting spectral method under study is unconditionally stable and conserves the position density. Moreover it is gauge invariant and time reversible when the corresponding Schrödinger equation is. Numerical tests are presented for linear, for weak/strong focusing/defocusing nonlinearities, for the Gross-Pitaevskii equation and for current-relaxed quantum hydrodynamics. The tests are geared towards understanding admissible meshing strategies for obtaining ‘correct’ physical observables in the semi-classical regimes. Furthermore, comparisons between the solutions of the nonlinear Schrödinger equation and its hydrodynamic semiclassical limit are presented.

Keywords: Time-splitting spectral method; Schrödinger equation; semi-classical regime; admissible meshing strategy; physical observable (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-0113-8_2

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DOI: 10.1007/978-1-4615-0113-8_2

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