On the Born-Oppenheimer expansion for polyatomic molecules
type: Item
instance of: scholarly article
title: On the Born-Oppenheimer expansion for polyatomic molecules
zbMATH Open document ID: 0754.35099
DOI: 10.1007/BF02099269
author: André Martinez
author: Xue Ping Wang
author: M. Klein
author: Ruedi Seiler
published in: Communications in Mathematical Physics
publication date: 1992-09-26T00:00:00Z
review text: The Schrödinger operator \(P(h)\) for a polyatomic molecule with Coulomb interactions is discussed in the limit where the mass ratio \(h^ 2\) of electronic to nuclear mass tends to zero. Asymptotic expansions of eigenvalues and eigenfunctions of \(P(h)\) are obtained to all orders in \(h\). This justifies the Born-Oppenheimer expansion: \textit{M. Born} and \textit{R. Oppenheimer} [Annal. Phys. 84, 457 ff. (1927)] in the physically relevant case.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 81V55
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 54731
zbMATH Keywords: polyatomic molecule
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: Born-Oppenheimer expansion
reviewed by: Joachim Asch
MaRDI profile type: Publication
cites work: Q3969238
cites work: A class of analytic perturbations for one-body Schrödinger Hamiltonians
cites work: Q3961493
cites work: A mathematical approach to the effective Hamiltonian in perturbed periodic problems
cites work: Multiple wells in the semi-classical limit I
cites work: Q3793072
cites work: Q3756727
cites work: Q3756006
cites work: On the mathematical theory of predissociation
cites work: Estimations de l'effet tunnel pour le double puits. (Estmates of tunneling for the double wells)
cites work: Resonances in Born-Oppenheimer approximation. II: Length of resonances.
full work available at URL: https://doi.org/10.1007/bf02099269
OpenAlex ID: W2018094839
description: scientific article; zbMATH DE number 54731