Choosing step sizes for perturbative methods of solving the Schrödinger equation

DOI10.1016/0021-9991(80)90182-5zbMath0457.65058OpenAlexW2016812456MaRDI QIDQ1151246

L. Gr. Ixaru, M. S. Popa, M. I. Cristu

Publication date: 1980

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(80)90182-5

zbMATH Keywords

algorithmserror boundsperturbative methodsone-dimensional Schrödinger equation

Mathematics Subject Classification ID

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)

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Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday, A highly convergent perturbative method for the solution of systems of coupled equations arising from the Schrödinger equation, A four-step method for the numerical solution of the Schrödinger equation, Automatic solution of Sturm-Liouville problems using the Pruess method, Automatic solution of regular and singular vector Sturm-Liouville problems

Cites Work

• A first-order perturbative numerical method for the solution of the radial Schrödinger equation
• Comparison of perturbation and direct-numerical-integration techniques for the calculation of phase shifts for elastic scattering
• Practical points concerning the solution of the Schrödinger equation
• A new method for the solution of the Schrödinger equation
• The numerical solution of coupled differential equations arising from the Schrödinger equation
• Numerical solution of Mathieu's equation