The Hermite pseudospectral method for the two-dimensional Schrödinger equation with nonseparable potentials

DOI10.1016/j.camwa.2015.01.002zbMath1443.65386OpenAlexW2072682240MaRDI QIDQ2006031

H. Alıcı

Publication date: 8 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2015.01.002

zbMATH Keywords

quantum mechanical potentialstwo dimensional Schrödinger equationHermite pseudospectral methods

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Schrödinger operator, Schrödinger equation (35J10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (2)

A new unconditionally stable method for telegraph equation based on associated Hermite orthogonal functions ⋮ The Laguerre pseudospectral method for the two-dimensional Schrödinger equation with symmetric nonseparable potentials

Uses Software

• Matlab

Cites Work

• The scaled Hermite-Weber basis in the spectral and pseudospectral pictures
• A new kind of discretization scheme for solving a two-dimensional time-independent Schrödinger equation
• Two-sided eigenvalue bounds for the spherically symmetric states of the Schrödinger equation
• An eigenfunction expansion for the Schrödinger equation with arbitrary non-central potentials
• The scaled Hermite--Weber basis still highly competitive
• Application of the pseudo-spectral method to 2D eigenvalue problems in elasticity
• Numerical solution of the two-dimensional time independent Schrödinger equation with Numerov-type methods
• Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Equations II. Unbounded Domains
• The Eigenvalues of Second-Order Spectral Differentiation Matrices
• Converging bounds for the eigenvalues of multiminima potentials in two-dimensional space
• Spectral Methods in MATLAB
• Algorithm 810: The SLEIGN2 Sturm-Liouville Code
• Calculation of Gauss Quadrature Rules

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