94-192 Graffi S., Paul T.

Quantum Intrinsically Degenerate and Classical Secular Perturbation Theory (98K, LaTeX) Jun 8, 94

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. For a class of smooth perturbation of the resonant harmonic oscillator in two degrees of freedom the quantum degenerate perturbation theory is explicitly constructed by quantization of the corresponding classical secular expansion. This result is based upon two identifications, which allow us to apply the quasi-modes construction: the unperturbed subspaces of fixed principal quantum number with the quantization of the K\"ahler manifolds defined by the classical constant energy surfaces, and the principal symbol of the perturbing operator in this subspace with the classical resonant normal form.

Files: 94-192.tex