Generalized Fourier transform for Schrödinger operators with potentials of order zero

DOI10.1006/jfan.1999.3432zbMath0937.35033OpenAlexW2078810179MaRDI QIDQ1807747

Jaime Cruz-Sampedro, Shmuel Agmon, Ira W. Herbst

Publication date: 23 May 2000

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3432

zbMATH Keywords

Schrödinger operatorscattering theorygeneralized Fourier transformation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Schrödinger operator, Schrödinger equation (35J10) General harmonic expansions, frames (42C15) Quantum scattering theory (81U99) Scattering theory of linear operators (47A40)

Related Items (14)

Quantum Scattering for Potentials Independent of |x|: Asymptotic Completeness for High and Low Energies ⋮ Spectral asymptotics for the Schrödinger operator with a non-decaying potential ⋮ Smooth Spectral Calculus ⋮ Schrödinger-like operators and the eikonal equation ⋮ On spectral theory for Schrödinger operators with operator-valued potentials ⋮ Global solutions to the eikonal equation ⋮ Energy concentration and Sommerfeld condition for Helmholtz and Liouville equations. ⋮ Divergence-type Operators: Spectral Theory and Spacetime Estimates ⋮ EIGENFUNCTION EXPANSIONS AND SPACETIME ESTIMATES FOR GENERATORS IN DIVERGENCE-FORM ⋮ Renormalized two-body low-energy scattering ⋮ Geometric Scattering for Schrödinger Operators with Asymptotically Homogeneous Potentials of Order Zero ⋮ Stationary scattering theory for repulsive Hamiltonians ⋮ Scattering theory for multistate Schrödinger operators ⋮ Stationary scattering theory on manifolds

Cites Work

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• Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators
• Schrödinger operators with a nonspherical radiation condition
• Spectral analysis of N-body Schrödinger operators
• Absence of singular continuous spectrum for certain self-adjoint operators
• A stationary approach to the existence and completeness of long-range wave operators
• Free channel Fourier transform in the long-range \(N\)-body problem
• Zur Theorie der Schwingungsgleichung mit variablen Koeffizienten in Außengebieten
• Das asymptotische Verhalten von Lösungen eines Typs von Differentialgleichungen
• Spectral and Scattering Theory for Schrodinger Operators with Potentials Independent of | x |
• On eikonal equations associated with schrodinger operators with nonspherical radiation conditions
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
• \(C_0\)-groups, commutator methods and spectral theory of \(N\)-body Hamiltonians

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