WKB wave functions for a nonseparable Hamiltonian

Abstract

The extended WKB method recently presented is applied to the construction of a high-lying semiclassical wave function, corresponding to the quantum numbers (30,30), for the Barbanis Hamiltonian, a well-known two-dimensional nonseparable system; the results are compared with the semiclassical wave function obtained, for the same state, by Davis and Heller, by means of the coherent Gaussians method. The extended WKB method shows that the semiclassical wave function is the sum of four wave functions, differing on parts of the classically allowed region, each of these separately satisfying the Einstein–Brillouin–Keller quantization rules. The results presented here show that our method, which is the direct extension to integrable nonseparable Hamiltonians of the usual WKB scheme, is suitable for the semiclassical quantization of high-lying states also, and enables a closer investigation of the fine structures of the semiclassical wave functions.