Numerical solution of the 3D time dependent Schrödinger equation in spherical coordinates: Spectral basis and effects of split-operator technique

DOI10.1016/j.cam.2008.06.015zbMath1159.65349OpenAlexW2090001710MaRDI QIDQ1003998

Tore Birkeland, Tor Sørevik, Gabriel Okša

Publication date: 2 March 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2008.06.015

zbMATH Keywords

Chebyshev polynomialsvariable transformationoperator splittingtime dependent Schrödinger equationspectral approximationsplit stepsingulaumerical experimentsr Coulomb potential

Mathematics Subject Classification ID

Strong interaction, including quantum chromodynamics (81V05) PDEs in connection with quantum mechanics (35Q40) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (2)

Simple, accurate, and efficient implementation of 1-electron atomic time-dependent Schrödinger equation in spherical coordinates ⋮ A time-splitting pseudospectral method for the solution of the Gross-Pitaevskii equations using spherical harmonics with generalised-Laguerre basis functions

Cites Work

• Solution of the Schrödinger equation by a spectral method
• Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: A comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions
• Error bounds for exponential operator splittings
• Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation
• Splitting methods
• Fourth-Order Time-Stepping for Stiff PDEs
• On the Construction and Comparison of Difference Schemes
• Unnamed Item

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