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 $\alpha=1$.