Calculation of the Landau quasiclassical exponent from the Fourier components of classical functions

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Abstract
In this paper, we show that the Landau quasiclassical exponent, which determines an exponentially small transition amplitude, can be recovered from the Fourier analysis of classical functions for both one-dimensional and three-dimensional cases. This finding renders unnecessary the analytical continuation of the potential-energy function into the classically inaccessible region of the configuration space. In addition, we present a criterion for the applicability of the Landau method on the basis of the correspondence-principle matrix elements and discuss the relation between this method and the phase-integral approach.