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Title: New method for computation of discrete spectrum of radical Schrödinger operator (English)
Author: Úlehla, Ivan
Author: Havlíček, Miloslav
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 25
Issue: 5
Year: 1980
Pages: 358-372
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: A new method for computation of eigenvalues of the radial Schrödinger operator $-d^2/dx^2+v(x), x\geq 0$ is presented. The potential $v(x)$ is assumed to behave as $x^{-2+\epsilon}$ if $x\rightarrow 0_+$ and as $x^{-2-\epsilon}$ if $x\rightarrow +\infty, \epsilon \geq 0$. The Schrödinger equation is transformed to a non-linear differential equation of the first order for a function $z(x,\aleph)$. It is shown that the eigenvalues are the discontinuity points of the function $z(\infty, \aleph)$. Moreover, it is shown how to obtain an arbitrarily accurate approximation of eigenvalues. The method seems to be much more economical in comparison with other known methods used in numerical computations on computers. (English)
Keyword: computation of discrete spectrum
Keyword: quantum mechanical problem
MSC: 34B25
MSC: 34L99
MSC: 65L15
MSC: 81C05
MSC: 81Q10
idZBL: Zbl 0447.34025
idMR: MR0590489
DOI: 10.21136/AM.1980.103870
Date available: 2008-05-20T18:15:04Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] Z. S. Agranovich V. A. Marchenko: Inverse Scattering Theory Problem.N. York 1963.
Reference: [2] F. G. Tricomi: Differential Equations.Blackie and Son, 1961. Zbl 0101.05904, MR 0138812
Reference: [3] M. A. Naymark: Linejnye differencialnye operatory.Moskva, 1969.
Reference: [4] I. Úlehla: The nucleon-antinucleon bound states.Preprint CEN-Saciay, DPhPE 76-23.
Reference: I. Zborovský: Study of nucleon-antinucleon bound states.Diploma-thesis, Faculty of Matematics and Physics, Prague, 1978 (in Czech).
Reference: [5] J. Kurzweil: Ordinary Differential Equations.Praha 1978 (in Cezch). Zbl 0401.34001, MR 0617010
Reference: [6] F. Calogero: Variable phase approach to potential scattering.N. York, Ac. Press 1967. Zbl 0193.57501


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