Solution of the Schrödinger equation by a high order perturbation method based on a linear reference potential

DOI10.1016/j.cpc.2006.06.005zbMath1196.81127OpenAlexW2014410007MaRDI QIDQ709978

M. Rizea, L. Gr. Ixaru, Guido Vanden Berghe, Veerle Ledoux, Marnix van Daele

Publication date: 18 October 2010

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2006.06.005

zbMATH Keywords

eigenvalue problemerror analysisSchrödinger equationasymptotic expansionsperturbative correctionsairy functionsLP methodstep size adjusting

Mathematics Subject Classification ID

Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (11)

The accurate numerical solution of the Schrödinger equation with an explicitly time-dependent Hamiltonian ⋮ Coefficients perturbation methods for higher-order differential equations ⋮ Correction of eigenvalues estimated by the Legendre-Gauss tau method ⋮ Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics ⋮ Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation ⋮ Exponentially weighted Legendre-Gauss tau methods for linear second-order differential equations ⋮ Solving Sturm-Liouville problems by piecewise perturbation methods, revisited ⋮ Pseudospectral methods of solution of the Schrödinger equation ⋮ Efficient computation of the Airy propagators ⋮ Fast LP method for the Schrödinger equation ⋮ An improved tau method for a class of Sturm-Liouville problems

Uses Software

• Maple
• MATSLISE
• NAG
• SLCPM12
• Algorithm 838
• AIZ
• BIZ
• nag

Cites Work

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• CP methods of higher order for Sturm-Liouville and Schrödinger equations
• Comparison of numerical methods for solving the second-order differential equations of molecular scattering theory
• Piecewise perturbation methods for calculating eigensolutions of a complex optical potential
• CRCWFN: Coupled real Coulomb wavefunctions
• SLCPM12 -- a program for solving regular Sturm-Liouville problems
• CP methods and the evaluation of negative energy Coulomb Whittaker functions
• The error analysis of the algebraic method for solving the Schrödinger equation
• MATSLISE
• Algorithm 644
• Algorithm 838

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