Numerical solutions of Schrödinger equations in ℝ3

DOI10.1002/num.20193zbMath1122.65088OpenAlexW2127677060MaRDI QIDQ3442831

Zhongyi Huang, Houde Han, Dongsheng Yin

Publication date: 23 May 2007

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.20193

zbMATH Keywords

numerical resultsfinite element methodtime-dependent Schrödinger equationartificial boundaryexact boundary condition

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (7)

Fast evaluation of exact transparent boundary condition for one-dimensional cubic nonlinear Schrödinger equation ⋮ Time-dependent simulations of quantum waveguides using a time-splitting spectral method ⋮ Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings ⋮ A survey on artificial boundary method ⋮ Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential ⋮ An analysis of the finite-difference method for one-dimensional Klein-Gordon equation on unbounded domain ⋮ Transparent boundary conditions and numerical computation for singularly perturbed telegraph equation on unbounded domain

Cites Work

• Exact artifical boundary conditions for the Schrödinger equation in \(\mathbb R ^2\)
• Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability
• Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions

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