A multi-channel scattering theory for some time dependent Hamiltonians, charge transfer problem

DOI10.1007/BF01222515zbMath0437.47008MaRDI QIDQ1141334

Kenji Yajima

Publication date: 1980

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

zbMATH Keywords

multi-channel wave operatorsSchrödinger equations with time dependent potentials

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) (n)-body potential quantum scattering theory (81U10) Scattering theory of linear operators (47A40)

Related Items (22)

The point-like limit for a NLS equation with concentrated nonlinearity in dimension three ⋮ Existence of solutions for Schrödinger evolution equations ⋮ Scattering theory for temporally inhomogeneous Hamilton equations in Hilbert space ⋮ Asymptotic transition probabilities ⋮ Asymptotic completeness for multiparticle dispersive charge transfer models ⋮ Dispersive charge transfer model with long-range quantum interactions ⋮ Charge transfer model and three body-scattering ⋮ Unnamed Item ⋮ Time boundedness of the energy for the charge transfer model ⋮ Space-time behavior of propagators for Schrödinger evolution equations with Stark effect ⋮ Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations with time-dependent potential ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Moving potentials and the completeness of wave operators. III: Existence and completeness ⋮ Strichartz estimates for charge transfer models ⋮ Unnamed Item ⋮ Soliton-Potential Interactions for Nonlinear Schrödinger Equation in $\mathbb{R}^3$ ⋮ Unnamed Item ⋮ Asymptotic completeness for a quantum particle in a Markovian short range potential ⋮ Endpoint Strichartz estimates for charge transfer Hamiltonians ⋮ Unnamed Item ⋮ Geometric methods in scattering theory of the charge transfer model

Cites Work

• Abstract stationary theory of multichannel scattering
• Scattering theory for Schrödinger equation with potential periodic in time
• Wave operators and similarity for some non-selfadjoint operators
• Relatively compact interactions in many particle systems
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