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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.

The eigenfunction problem in higher dimensions: Asymptotic theory