On the Born-Oppenheimer approximation of wave operators in molecular scattering theory

DOI10.1007/BF02097058zbMath0778.35088OpenAlexW2089876459MaRDI QIDQ1803942

X. P. Wang, Markus Klein, André Martinez

Publication date: 29 June 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02097058

zbMATH Keywords

Schrödinger operatorsemiclassical limitcluster Hamiltonian

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) PDEs in connection with quantum mechanics (35Q40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (15)

Phase space tunneling in multistate scattering ⋮ Unnamed Item ⋮ On the Born-Oppenheimer approximation of diatomic molecular resonances ⋮ The infinite time limit for the time-dependent Born-Oppenheimer approximation ⋮ Unnamed Item ⋮ Besov estimates in the high-frequency Helmholtz equation, for a non-trapping and \(C^{2}\) potential ⋮ Asymptotic distribution of resonances for matrix Schrödinger operator in one dimension ⋮ On the Born–Oppenheimer approximation of diatomic wave operators. II. Singular potentials ⋮ Unnamed Item ⋮ The Born–Oppenheimer Approximation: Straight-Up and with a Twist ⋮ On the mathematical treatment of the Born-Oppenheimer approximation ⋮ MOLECULAR PROPAGATION THROUGH SMALL AVOIDED CROSSINGS OF ELECTRON ENERGY LEVELS ⋮ Reduction Scheme for Semiclassical Operator-Valued Schrödinger Type Equation and Application to Scattering ⋮ Multicomponent Wentzel–Kramers–Brillouin approximation on arbitrary symplectic manifolds: A star product approach ⋮ Estimations de diffusion pour un opérateur de Klein-Gordon matriciel dépendant du temps

Cites Work

• Time-decay of scattering solutions and resolvent estimates for semiclassical Schrödinger operators
• The quasi-classical limit of quantum scattering theory
• Absence of singular continuous spectrum for certain self-adjoint operators
• Semiclassical resolvent estimates for \(N\)-body Schrödinger operators
• On the Born-Oppenheimer expansion for polyatomic molecules
• Time-Delay Operators in Semiclassical Limit. II. Short-Range Potentials
• Multiple wells in the semi-classical limit I
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the Born-Oppenheimer approximation of wave operators in molecular scattering theory