First-order perturbative numerical method for the solution of the radial Schroedinger equation

Journal Article · Wed Sep 01 04:00:00 EDT 1976 · J. Comput. Phys.; (United States)

DOI:https://doi.org/10.1016/0021-9991(76)90107-8· OSTI ID:7290096

Adam, G ^[1]; Ixaru, L G; Corciovei, A

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1. Univ., Geneva

A very simple perturbative numerical (PN) algorithm is developed for the solution of the radial Schroedinger equation, using first order perturbation theory along the lines previously developed by Gordon. This algorithm uses the same basic approximation (a step function approximation for the potential well) as that recently reported by Richl, Diestler, and Wagner. It shows, however, an O(h/sup 5/) rate of convergence in the step size h, as compared to the O(h/sup 4/) rate of convergence of the algorithm given in the above cited reference. A new feature of the PN approach to the solution of the Schroedinger equation, namely, the remarkable stability of the present PN algorithm against the round off errors is reported. A comparison with the Numerov method for eigenvalue problems proves the high efficiency of the present algorithm.

• OSTI ID: 7290096
• Journal Information: J. Comput. Phys.; (United States), Journal Name: J. Comput. Phys.; (United States) Vol. 22:1; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EIGENVALUES
ENERGY
EQUATIONS
PERTURBATION THEORY
POTENTIAL ENERGY
SCHROEDINGER EQUATION
STABILITY
WAVE EQUATIONS