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The Schrödinger equation as a singular perturbation problem†

Published online by Cambridge University Press:  14 November 2011

E. M. de Jager  and
T. Küpper
E. M. de Jager
Affiliation:
Department of Mathematics, University of Amsterdam, Netherlands
T. Küpper
Affiliation:
Department of Mathematics, University of Cologne, Germany
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Synopsis

Comparisons have been made of the eigenvalues and the corresponding eigenfunctions of the eigenvalue problems

and

with φ ∈ C(-∞, +∞) and 0≦φ(x)≦C|x|i+1(1+|x|1), −∞<x<+∞ where i and l are arbitrary positive numbers with i≧2k≧2, k integer. In first approximation the eigenvalues λ and λ− and the corresponding eigenfunctions ψ and ψ are the same for ε→0; the error decreases whenever the exponent i increases.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 1 - 11
Copyright
Copyright © Royal Society of Edinburgh 1978

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