Semiclassical quantization via adiabatic switching. I. Choice of tori and initial conditions for two-dimensional systems

A general theoretical base and a general strategy for implementing semiclassical quantization using the adiabatic-switching method are presented for two-dimensional systems. The method proposed does not depend on specialized coordinates, trajectory, or surfaces-of-section studies and is generalizable to multidimensional systems. The choice of the initial tori for the switching procedure is accomplished by simple diagonalizations of small-dimensional matrix representations of invariant operators obtained from perturbation theory. The method gives quantum energies at a useful level of accuracy for the vast majority of states in many of the well-known nonresonant and resonant Hamiltonian cases. Many eigenvalues previously thought unobtainable when the adiabatic-switching method is used are obtained in a quite simple manner