Semiclassical quantization by using the method of adiabatic switching of the perturbation: Fermi resonance

Abstract

The method of adiabatic switching of perturbation is applied in semiclassical calculations of the eigenvalues of classically near-integrable Hamiltonian describing a two-dimensional coupled oscillator whose dynamics is dominated by an intrinsic 2:1 resonance. At low-to-intermediate excitations the semiclassical eigenvalues are generally in good agreement with quantum-variational results. Even at high excitations, close to the classical escape energy, useful information on the location of quantal levels can be obtained. Limitations of the method are discussed.