Semiclassical quantization of Nonseparable Hamiltonian Systems

The methods for the primitive and uniform semiclassical quantization of nonseparable Hamiltonian systems are developed. The transformation of integrable nonseparable Hamiltonians to angle action variables by a sequence of Van Vleck transformations is described. The calculation of the primitive semiclassical eigenvalues by evaluating the transformed Hamiltonian at the quantized values of the actions is discussed. The uniform semiclassical eigenvalues, found by numerical evaluation of the uniform semiclassical quantization condition are calculated.