Quantum Averaging I: Poincaré--von Zeipel is Rayleigh--Schrödinger

Abstract

An exact analogue of the method of averaging in classical mechanics is constructed for self--adjoint operators. It is shown to be completely equivalent to the usual Rayleigh--Schrödinger perturbation theory but gives the sums over intermediate states in closed form expressions. The anharmonic oscillator and the Henon--Heiles system are treated as examples to illustrate the quantum averaging method.

12 pages, LaTeX, to appear in Journ. Phys. A

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