Magnus-factorized method for numerical solving the time-dependent Schrödinger equation

DOI10.1016/S0010-4655(99)00225-8zbMath0962.65103MaRDI QIDQ1973534

I. V. Puzynin, Alexei V. Selin, S. I. Vinitskij

Publication date: 31 May 2001

Published in: Computer Physics Communications (Search for Journal in Brave)

zbMATH Keywords

stabilityCauchy problemtime dependent Schrödinger equationMagnus expansionhigh-order finite differences

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

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Preserving geometric properties of the exponential matrix by block Krylov subspace methods ⋮ Fourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potential ⋮ Symbolic algorithm for factorization of the evolution operator of the time-dependent Schrödinger equation ⋮ Qprop: A Schrödinger-solver for intense laser-atom interaction ⋮ Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients ⋮ A new investigation of the extended Krylov subspace method for matrix function evaluations

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