Once again: Instanton method vs. WKB

Abstract

A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lam$\acute{e}$ potential (derived from representations of a finite dimensional matrix expressed in terms of $su(2)$ generators) with the results of the tight--binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lam$\acute{e}$ potential as well as others the WKB--related method of matched asymptotic expansions yields the exact instanton result as a result of boundary conditions imposed on wave functions which are matched in domains of overlap.

10 pages, no figures. References list revised according to JHEP

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