Once again: Instanton method vs. WKB
H. J. W. Müller-Kirsten, Jian-zu Zhang, Yunbo Zhang
Abstract
A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lam 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 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.
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