A general reduction scheme for the time-dependent Born-Oppenheimer approximation.

DOI10.1016/S1631-073X(02)02212-4zbMath1079.81524OpenAlexW2018939220MaRDI QIDQ1598485

André Martinez, Vania Sordoni

Publication date: 2002

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1631-073x(02)02212-4

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Molecular physics (81V55)

Related Items (19)

Computing quantum dynamics in the semiclassical regime ⋮ On the Born-Oppenheimer approximation of diatomic molecular resonances ⋮ Semiclassical determination of exponentially small intermode transitions for 1 + 1 spacetime scattering systems ⋮ Adiabatic approximation for a two-level atom in a light beam ⋮ Semiclassical limit for multistate Klein–Gordon systems: almost invariant subspaces, and scattering theory ⋮ Gell-Mann and low formula for degenerate unperturbed states ⋮ Unnamed Item ⋮ Effective dynamics for particles coupled to a quantized scalar field ⋮ Superadiabatic transitions in quantum molecular dynamics ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ Spontaneous decay of resonant energy levels for molecules with moving nuclei ⋮ On the mathematical treatment of the Born-Oppenheimer approximation ⋮ Weyl formulae for the Robin Laplacian in the semiclassical limit ⋮ Reduction Scheme for Semiclassical Operator-Valued Schrödinger Type Equation and Application to Scattering ⋮ The time-dependent Born-Oppenheimer approximation ⋮ Born-Oppenheimer approximation for an atom in constant magnetic fields ⋮ Effective Hamiltonians for Constrained Quantum Systems ⋮ The adiabatic limit of the connection Laplacian ⋮ Exponentially accurate semiclassical asymptotics of low-lying eigenvalues for \(2\times 2\) matrix Schrödinger operators

Cites Work

• Unnamed Item
• Autour de l'approximation semi-classique. (Around semiclassical approximation)
• On the Born-Oppenheimer expansion for polyatomic molecules
• Fourier integral operators with complex phase functions and parametrix for an interior boundary value problem
• Semiclassical limit for multistate Klein–Gordon systems: almost invariant subspaces, and scattering theory
• Adiabatic decoupling and time-dependent Born-Oppenheimer theory
• An introduction to semiclassical and microlocal analysis
• A time-dependent Born-Oppenheimer approximation with exponentially small error estimates.

This page was built for publication: A general reduction scheme for the time-dependent Born-Oppenheimer approximation.