SEMI-CLASSICAL CALCULATION OF BOUND-STATES IN MULTIDIMENSIONAL SYSTEMS WITH FERMI RESONANCE

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. © 1979 American Institute of Physics.