A perturbation approach to finite difference methods

DOI10.1007/S10910-010-9723-1zbMath1202.81041OpenAlexW2069356811MaRDI QIDQ607594

A. Lakhlifi, John P. Killingbeck

Publication date: 22 November 2010

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

Full work available at URL: https://doi.org/10.1007/s10910-010-9723-1

zbMATH Keywords

finite differencesquantum mechanicsenergy levels

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Molecular physics (81V55) Finite difference and finite volume methods for ordinary differential equations (65L12)

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Calculating probabilities without quadrature ⋮ A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation ⋮ High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation

Cites Work

• A new methodology for the development of numerical methods for the numerical solution of the Schrödinger equation
• A new methodology for the construction of numerical methods for the approximate solution of the Schrödinger equation
• Stable forward shooting for eigenvalues and expectation values
• The virial finite difference method.
• Shooting methods for the Schrodinger equation
• Boolean functions and finite difference eigenvalues
• Finite difference order doubling in two dimensions

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