Solving the 1-, 2-, and 3-dimensional Schrödinger equation for multiminima potentials using the Numerov-Cooley method. An extrapolation formula for energy eigenvalues

DOI10.1016/0021-9991(89)90039-9zbMath0676.65130OpenAlexW2044687443MaRDI QIDQ1122969

Michael Eckert

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0021-9991(89)90039-9

zbMATH Keywords

numerical exampleseigenfunctionsSchrödinger equationRichardson extrapolationenergy eigenvaluesmultiminima potentialsNumerov-Cooley algorithm

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Schrödinger operator, Schrödinger equation (35J10) Applications to the sciences (65Z05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Ordinary differential operators (34L99)

Related Items (2)

NuSol -- numerical solver for the 3D stationary nuclear Schrödinger equation ⋮ Numerical solving of the vibrational time-independent Schrödinger equation in one and two dimensions using the variational method

Cites Work

• Unnamed Item
• Error sources in the standard numerical integration of the Schrödinger equation: An improved method
• On quantal bound state solutions and potential energy surface fitting. A comparison of the finite element, Numerov-Cooley and finite difference methods
• On the numerical solution of Schrödinger's radial equation
• On the numerical integration of the Schrödinger equation with a double- minimum potential
• Practical points concerning the solution of the Schrödinger equation
• An Improved Eigenvalue Corrector Formula for Solving the Schrodinger Equation for Central Fields
• The Numerov method and singular potentials

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