SEMICLASSICAL QUANTIZATION OF THE SPECTROSCOPISTS HAMILTONIAN FOR COUPLED VIBRATIONAL-MODES

Exact analytical semiclassical quantization of the regular Hamiltonian for two vibrational modes coupled by a single m:n resonance (m + n le ss-than-or-equal-to 4) is described. This requires analytical calculat ion of the two action integrals of the system. A simple analytical for mula is obtained, which works for all the trajectories for the four 1: 1, 1:2, 1:3 and 2:2 resonances. Moreover, it is shown that numerical c alculation of Maslov indexes can also be avoided. Some discrepancies b etween quantum and semiclassical results are pointed out.