The Gaussian wave packet transform: efficient computation of the semi-classical limit of the Schrödinger equation. I: Formulation and the one dimensional case

DOI10.1016/j.jcp.2012.08.018zbMath1286.35216OpenAlexW2011618387MaRDI QIDQ2449733

Publication date: 12 May 2014

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2012.08.018

zbMATH Keywords

Schrödinger equation splitting methods semi-classical limit

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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Asymptotic-preserving schemes for multiscale physical problems ⋮ Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations ⋮ An improved semi-Lagrangian time splitting spectral method for the semi-classical Schrödinger equation with vector potentials using NUFFT ⋮ The Gaussian wave packet transform: efficient computation of the semi-classical limit of the Schrödinger equation. II: Multidimensional case ⋮ Fast multiscale Gaussian beam methods for wave equations in bounded convex domains ⋮ Numerical approximation of the Schrödinger equation with the electromagnetic field by the Hagedorn wave packets ⋮ Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs ⋮ The Gaussian Wave Packet Transform for the Semi-Classical Schrödinger Equation with Vector Potentials ⋮ Asymptotic approximations for the phase space Schrödinger equation

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