Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis

DOI10.1515/rnam-2016-0005zbMath1333.65098OpenAlexW2964230171MaRDI QIDQ5962825

Alexander Zlotnik, Ilya Zlotnik

Publication date: 24 February 2016

Published in: Russian Journal of Numerical Analysis and Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/rnam-2016-0005

zbMATH Keywords

finite difference schemesnumerical experimenttime-dependent Schrödinger equationdiscrete convolutiondiscrete transparent boundary conditionsNumerov schemesemi-discrete transparent boundary conditions

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (6)

On a splitting higher-order scheme with discrete transparent boundary conditions for the Schrödinger equation in a semi-infinite parallelepiped ⋮ Error Estimates of the Crank-Nicolson-Polylinear FEM with the Discrete TBC for the Generalized Schrödinger Equation in an Unbounded Parallelepiped ⋮ The Numerov-Crank-Nicolson scheme on a non-uniform mesh for the time-dependent Schrödinger equation on the half-axis ⋮ On a Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip ⋮ ON THE ACCURACY OF SOME ABSORBING BOUNDARY CONDITIONS FOR THE SCHRODINGER EQUATION ⋮ A THREE-LEVEL PARALLELISATION SCHEME AND APPLICATION TO THE NELDER-MEAD ALGORITHM

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