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 |
Keywords:
Bargmann representation; Schrödinger equation; harmonic oscillator; classical Hamilton-Jacobi equation; perturbation theory; Rayleigh- Schrödinger series; semiclassical limitReferences:
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