CP methods for the Schrödinger equation revisited

DOI10.1016/S0377-0427(97)00218-5zbMath0909.65045MaRDI QIDQ1385051

L. Gr. Ixaru, Guido Vanden Berghe, H. E. De Meyer

Publication date: 12 April 1999

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

eigenvalue problemerror analysisinitial value problemSchrödinger equationconstant perturbation method

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) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (20)

Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday ⋮ Numerical methods for the eigenvalue determination of second-order ordinary differential equations ⋮ The accurate numerical solution of the Schrödinger equation with an explicitly time-dependent Hamiltonian ⋮ Reliable computation of the eigenvalues of the discrete KdV spectrum ⋮ Numerical approach of some three-body problems ⋮ The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equations ⋮ A Chebyshev pseudospectral multidomain method for the soliton solution of coupled nonlinear Schrödinger equations ⋮ Explicit Numerov type methods with reduced number of stages. ⋮ Exponentially weighted Legendre-Gauss tau methods for linear second-order differential equations ⋮ An exponentially convergent functional-discrete method for solving Sturm-Liouville problems with a potential including the Dirac \(\delta\)-function ⋮ CP methods and the evaluation of negative energy Coulomb Whittaker functions ⋮ New numerical method for the eigenvalue problem of the 2D Schrödinger equation ⋮ CP methods of higher order for Sturm-Liouville and Schrödinger equations ⋮ RCMS: Right correction Magnus series approach for oscillatory ODEs ⋮ \(CPM\{P,N\}\) methods extended for the solution of coupled channel Schrödinger equations ⋮ Spectral corrections for Sturm-Liouville problems ⋮ SLCPM12 -- a program for solving regular Sturm-Liouville problems ⋮ CP methods for the Schrödinger equation ⋮ LILIX -- a package for the solution of the coupled channel Schrödinger equation ⋮ Matslise 2.0

Uses Software

• Mathematica
• SLDRIVER
• SLEDGE

Cites Work

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• Correction of Numerov's eigenvalue estimates
• On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems
• Automatic solution of Sturm-Liouville problems using the Pruess method
• Piecewise perturbation methods for calculating eigensolutions of a complex optical potential
• Automatic Solution of the Sturm-Liouville Problem
• Mathematical software for Sturm-Liouville problems
• Accurate computation of higher Sturm-Liouville eigenvalues

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