equations (cf. [AKT1]), the exact WKB analysis provides us with a powerful tool for studying global behavior of solutions of linear ordinary di erential equations. To generalize such an analysis to nonlinear equations, T. Kawai (RIMS, Kyoto Univ.), T. Aoki (Kinki Univ.) and the author have developed the WKB theory for Painlev e equations with a large parameter in our series of articles ([KT1], ...

Two types of semiclassical calculations have been used to study quantum effects in black hole backgrounds, the WKB and the mean field approaches. In this work we systematically reconstruct the logical implications of both methods on quantum black hole physics and provide the link between these two approaches. Our conclusions completely support our previous findings based solely on the WKB metho...

This article is devoted to the description of eigenvalues and eigenfunctions magnetic Laplacian in semiclassical limit via complex WKB method. Under assumption that field has a unique non-degenerate minimum, we construct local approximations for on general surface. Furthermore, case Euclidean plane, with radially symmetric field, are approximated an exponentially weighted space.

In this paper, the WKB method is extended to be applicable for conformable Hamiltonian systems where concept of operator with fractional order $\alpha$ used. The approximation $\alpha$-wavefunction derived when potential slowly varying in space. paper furnished some illustrative examples demonstrate method. quantities form are found inexact agreement traditional $\alpha=1$.