Semi-classical bounds for resolvents of schrödinger operators and asymptotics for scattering phases

DOI10.1080/03605308408820355zbMath0561.35021OpenAlexW2084403660MaRDI QIDQ5186046

Didier Robert, Hideo Tamura

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1080/03605308408820355

zbMATH Keywords

Schrödinger operatorscattering phasepositive energiesmicrolocal approximationBirman- Krein trace formulaprojected resolventSemiclassical bounds

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Schrödinger operator, Schrödinger equation (35J10) (2)-body potential quantum scattering theory (81U05)

Related Items (22)

Low energy asymptotics for Schrödinger operators with slowly decreasing potentials ⋮ Adiabatic Evolution and Shape Resonances ⋮ Approximation semi-classique de l'equation de Heisenberg. (Semi-classical approximation of the Heisenberg equation) ⋮ On the location of resonances for Schrödinger operators in the semiclassical limit. I: Resonances free domains ⋮ The shape resonance ⋮ Étude semi-classique d'observables quantiques ⋮ Time-decay of scattering solutions and resolvent estimates for semiclassical Schrödinger operators ⋮ Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation ⋮ A Time-Independent Approach for the Study of the Spectral Shift Function and an Application to Stark Hamiltonians ⋮ Unnamed Item ⋮ Breit–Wigner formula at barrier tops ⋮ Unnamed Item ⋮ Low energy resolvent estimates and continuity of time-delay operators ⋮ Semiclassical resolvent estimates for \(N\)-body Schrödinger operators ⋮ The spectrum of the scattering matrix near resonant energies in the semiclassical limit ⋮ Equidistribution of phase shifts in semiclassical potential scattering ⋮ Quantum evolution and classical flow in complex phase space ⋮ A note on the absence of resonances for Schrödinger operators ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles
• A construction of the fundamental solution for the Schrödinger equation
• An analogue of Weyl's formula for unbounded domains. III: An epilogue
• Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques
• A scattering theory for time-dependent long-range potentials
• The first variation of the scattering matrix
• The spectral function of an elliptic operator
• Asymptotic behalrior of the scattering phase for exterior domains
• Spectre D'Un hamiltonien quantique et mecanique classique
• The weyl calculus of pseudo-differential operators

This page was built for publication: Semi-classical bounds for resolvents of schrödinger operators and asymptotics for scattering phases