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The Schrödinger equation as a singular perturbation problem†
Published online by Cambridge University Press: 14 November 2011
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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