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A method is devised to calculate eigenvalues semiclassically for an anharmonic system whose two unperturbed modes are 2:1 degenerate. For some special states the periodic energy exchange between unperturbed modes is found to be very large. The quantum mechanical wave functions are examined and a correlation with the classical trajectories is described, both for quasiperiodic and the stochastic cases. A method used in the literature for calculating the stochastic limit is tested and found to break down when the present anharmonic system is separable.
Noid et al. (Mon,) studied this question.
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