Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation

DOI10.1007/s00211-013-0560-6zbMath1303.65075OpenAlexW2011800114MaRDI QIDQ2436539

George A. Hagedorn, Vasile Gradinaru

Publication date: 25 February 2014

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: http://doc.rero.ch/record/325620/files/211_2013_Article_560.pdf

zbMATH Keywords

convergencetime discretizationsemiclassical wavepacketssemiclassical time-dependent Schrödinger equation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Time-dependent Schrödinger equations and Dirac equations (35Q41) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items

Computing quantum dynamics in the semiclassical regime ⋮ Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime ⋮ Hagedorn wavepackets and Schrödinger equation with time-dependent, homogeneous magnetic field ⋮ Discretising the Herman-Kluk propagator ⋮ Non-Hermitian propagation of Hagedorn wavepackets ⋮ Compact schemes for laser-matter interaction in Schrödinger equation based on effective splittings of Magnus expansion ⋮ Symmetric Kronecker Products and Semiclassical Wave Packets ⋮ High order efficient splittings for the semiclassical time-dependent Schrödinger equation ⋮ The Hagedorn-Hermite correspondence ⋮ Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation ⋮ An error bound for the time-sliced thawed Gaussian propagation method

Cites Work

• Effective approximation for the semiclassical Schrödinger equation
• An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime
• From quantum to classical molecular dynamics: Reduced models and numerical analysis.
• Gaussian beam methods for the Schrödinger equation in the semi-classical regime: Lagrangian and Eulerian formulations
• Solution of the Schrödinger equation by a spectral method
• Raising and lowering operators for semiclassical wave packets
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation
• Error control for time-splitting spectral approximations of the semiclassical Schrodinger equation
• Computing Semiclassical Quantum Dynamics with Hagedorn Wavepackets
• Semi-Eulerian and High Order Gaussian Beam Methods for the Schrödinger Equation in the Semiclassical Regime

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