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The Schrödinger equation and canonical perturbation theory. (English) Zbl 0622.35071
Working in the Bargmann representation, the Schrödinger equation for a perturbed d-dimensional harmonic oscillator is rewritten as a classical Hamilton-Jacobi equation plus corrections under the form of a convergent power series in the Planck constant h. Then the canonical (Birchoff) perturbation theory is applied and related to the Rayleigh-Schrödinger series. The results are relevant for the study of the semiclassical limit.
Reviewer: G.Nenciu

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
81Q15 Perturbation theories for operators and differential equations in quantum theory
35J10 Schrödinger operator, Schrödinger equation
35B20 Perturbations in context of PDEs
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