Abstract
A recently proposed extension of the WKB method to integrable but non-separable Hamiltonian systems, based on the construction of global solutions of Dirichlet problems for the Hamilton - Jacobi equation, is applied to the construction of semiclassical wavefunctions for the Barbanis Hamiltonian. The wavefunctions obtained are compared with those generated for the same system, by means of the coherent Gaussian method, by Davis and Heller. It is shown that when the caustics are smooth curves, there is no energy degeneration, and the semiclassical wavefunctions obtained by the extended WKB method agree with those by Davis and Heller. But if internal caustics are present and to the same semiclassical energy level correspond, not simply to one as in the coherent Gaussian method, but several (four in the example investigated) WKB wavefunctions, they differ in the regions inside the internal caustics.
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