The scaled Hermite-Weber basis in the spectral and pseudospectral pictures

DOI10.1007/s10910-005-5826-5zbMath1217.65153OpenAlexW1995772294MaRDI QIDQ551995

H. Alıcı, Hasan Taşeli

Publication date: 21 July 2011

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-005-5826-5

zbMATH Keywords

Schrödinger operatorHermite collocation pointsHermite-Weber functionsquantum mechanical oscillatorssingular Sturm-Liouville problems on the real linespectral and pseudospectral methods

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (7)

A Rayleigh-Ritz method for numerical solutions of linear Fredholm integral equations of the second kind ⋮ The Laguerre pseudospectral method for the reflection symmetric Hamiltonians on the real line ⋮ General solution of the Schrödinger equation for some trigonometric potentials ⋮ Matlab package for the Schrödinger equation ⋮ The Hermite pseudospectral method for the two-dimensional Schrödinger equation with nonseparable potentials ⋮ Pseudospectral methods for solving an equation of hypergeometric type with a perturbation ⋮ Inverse Sturm–Liouville problems with pseudospectral methods

Cites Work

• The quadrature discretization method (QDM) in comparison with other numerical methods of solution of the Fokker-Planck equation for electron thermalization
• The scaled Hermite--Weber basis still highly competitive
• The eigenvalues of Hermite and rational spectral differentiation matrices
• Accurate numerical bounds for the spectral points of singular Sturm-Liouville problems over \(-\infty< x<\infty\)
• Generation of Pseudospectral Differentiation Matrices I
• The Hermite Spectral Method for Gaussian-Type Functions

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