The eigenfunction problem in higher dimensions: Asymptotic theory
- 1 December 1985
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 82 (24) , 8275-8278
- https://doi.org/10.1073/pnas.82.24.8275
Abstract
The spectral problem for linear operators on fully infinite domains is considered. A transformation first introduced by Wigner is used to show a number of asymptotic results. The method leads to a WKB (Wentzel-Kromers-Brillouin) theory for operators in more than one dimension. This includes practical tools for the approximate evaluation of spectra and eigenfunctions. Several general examples are developed.Keywords
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