The Schrödinger equation and canonical perturbation theory
type: Item
instance of: scholarly article
title: The Schrödinger equation and canonical perturbation theory
zbMATH Open document ID: 0622.35071
DOI: 10.1007/BF01210701
author: Thierry Paul
author: Sandro Graffi
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 81Q15
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35B20
zbMATH DE Number: 4008980
zbMATH Keywords: Bargmann representation
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: harmonic oscillator
zbMATH Keywords: classical Hamilton-Jacobi equation
zbMATH Keywords: perturbation theory
zbMATH Keywords: Rayleigh- Schrödinger series
zbMATH Keywords: semiclassical limit
reviewed by: Gheorghe Nenciu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01210701
OpenAlex ID: W2017964812
description: scientific article; zbMATH DE number 4008980