Reduction Scheme for Semiclassical Operator-Valued Schrödinger Type Equation and Application to Scattering

DOI10.1081/PDE-120024361zbMath1274.35073MaRDI QIDQ4421467

Vania Sordoni

Publication date: 27 August 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (7)

Adiabatic approximation for a two-level atom in a light beam ⋮ Semiclassical limit for multistate Klein–Gordon systems: almost invariant subspaces, and scattering theory ⋮ Effective dynamics for particles coupled to a quantized scalar field ⋮ 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

Cites Work

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• Mapping properties of wave and scattering operators for two-body Schrödinger operators
• A general reduction scheme for the time-dependent Born-Oppenheimer approximation.
• Phase space tunneling in multistate scattering
• Linear adiabatic theory. Exponential estimates
• On the Born-Oppenheimer approximation of wave operators in molecular scattering theory
• Pseudo-differential operators and Gevrey classes
• Scattering amplitude for dirac operators
• Semiclassical limit for multistate Klein–Gordon systems: almost invariant subspaces, and scattering theory

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