Time-decay of scattering solutions and resolvent estimates for semiclassical Schrödinger operators

DOI10.1016/0022-0396(88)90032-0zbMath0651.35022OpenAlexW2028710423MaRDI QIDQ1106402

Xue Ping Wang

Publication date: 1988

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(88)90032-0

zbMATH Keywords

estimatesdecaysemiclassicalinitial datashort-rangenon- trapping potentialsreal potential

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Schrödinger operator, Schrödinger equation (35J10)

Related Items (18)

Low energy asymptotics for Schrödinger operators with slowly decreasing potentials ⋮ Phase space tunneling in multistate scattering ⋮ Unnamed Item ⋮ High energy resolvent estimates for generalized many-body Schrödinger operators ⋮ Besov estimates in the high-frequency Helmholtz equation, for a non-trapping and \(C^{2}\) potential ⋮ Semiclassical limit for multistate Klein–Gordon systems: almost invariant subspaces, and scattering theory ⋮ Asymptotic expansion in time of the Schrödinger group on conical manifolds ⋮ Semiclassical measure for the solution of the dissipative Helmholtz equation ⋮ Semiclassical analysis of quantum asymptotic fields in the Yukawa theory ⋮ Semiclassical estimates on resolvents of Schrödinger operators with homogeneous electric field ⋮ Unnamed Item ⋮ The radiation condition at infinity for the high-frequency Helmholtz equation with source term: a wave-packet approach ⋮ Time-Delay Operators in Semiclassical Limit. II. Short-Range Potentials ⋮ On the Born-Oppenheimer approximation of wave operators in molecular scattering theory ⋮ Unnamed Item ⋮ Uniform resolvent estimates for a non-dissipative Helmholtz equation ⋮ Unnamed Item ⋮ High-frequency limit of the Helmholtz equation with variable refraction index

Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles
• A construction of the fundamental solution for the Schrödinger equation
• Propagation properties of quantum scattering states
• High energy resolvent estimates. II: Higher order elliptic operators
• Micro-local resolvent estimates for 2-body Schrödinger operators
• Approximation semi-classique de l'equation de Heisenberg. (Semi-classical approximation of the Heisenberg equation)
• Differentiability of generalized Fourier transforms associated with Schrödinger operators
• On the asymptotic distribution of the eigenvalues of pseudodifferential operators in \(R^n\)
• Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques
• A general calculus of pseudodifferential operators
• Local decay of scattering solutions to Schrödinger's equation
• Propagation Estimates for Schrodinger-Type Operators
• Étude semi-classique d'observables quantiques
• Spectre D'Un hamiltonien quantique et mecanique classique
• Proprietes asymptotiques du spectre dioperateurs pseuwdifferentiels sur IRⁿ
• ON THE SHORT WAVE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF STATIONARY PROBLEMS AND THE ASYMPTOTIC BEHAVIOUR ASt→ ∞ OF SOLUTIONS OF NON-STATIONARY PROBLEMS
• Semi-classical bounds for resolvents of schrödinger operators and asymptotics for scattering phases
• A Class of Bounded Pseudo-Differential Operators

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