 94192 Graffi S., Paul T.
 Quantum Intrinsically Degenerate and Classical
Secular Perturbation Theory
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Jun 8, 94

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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 quasimodes 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.
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