Low energy asymptotics for Schrödinger operators with slowly decreasing potentials
From MaRDI portal
Publication:1325575
DOI10.1007/BF02099413zbMath0812.35110OpenAlexW1997525702MaRDI QIDQ1325575
Publication date: 14 May 1995
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02099413
resolventspectral propertiessemiclassical methodsSchrödinger semigrouppseudodifferential operator calculus
Spectrum, resolvent (47A10) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (2)-body potential quantum scattering theory (81U05)
Related Items
A remark on Strichartz estimates for Schrödinger equations with slowly decaying potentials ⋮ Asymptotic expansion in time of the Schrödinger group on conical manifolds ⋮ Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities ⋮ Quantum systems at the brink: existence of bound states, critical potentials, and dimensionality ⋮ Two-body threshold spectral analysis, the critical case ⋮ Strichartz estimates for Schrödinger equations with slowly decaying potentials ⋮ Zero-energy bound state decay for non-local Schrödinger operators ⋮ Some improvements in the method of the weakly conjugate operator ⋮ Zero energy asymptotics of the resolvent for a class of slowly decaying potentials ⋮ Limiting absorption principle for some long range perturbations of Dirac systems at threshold energies ⋮ Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential ⋮ Semiclassical analysis of low and zero energy scattering for one-dimensional Schrödinger operators with inverse square potentials ⋮ Gevrey estimates of the resolvent and sub-exponential time-decay for the heat and Schrödinger semigroups ⋮ Low Frequency Estimates and Local Energy Decay for Asymptotically Euclidean Laplacians ⋮ Potentials for non-local Schrödinger operators with zero eigenvalues ⋮ Sommerfeld Radiation Condition at Threshold
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Semiclassical analysis of low lying eigenvalues. II: Tunneling
- Spectral stability under tunneling
- Decay rates of scattering states for Schrödinger operators
- Time-decay of scattering solutions and resolvent estimates for semiclassical Schrödinger operators
- Spectral properties of Schrödinger operators and time-decay of the wave functions results in \(L^2(\mathbb{R}^m),\;m\geq 5\)
- Spectral properties of Schrödinger operators and time-decay of the wave functions
- Spectral analysis of N-body Schrödinger operators
- Absence of singular continuous spectrum for certain self-adjoint operators
- Asymptotic expansions in time for solutions of Schrödinger-type equations
- Sharp propagation estimates for \(N\)-particle systems
- The low energy scattering for slowly decreasing potentials
- Multiple wells in the semi-classical limit I
- Shape resonances for distortion analytic schrödinger operators
- Semi-classical bounds for resolvents of schrödinger operators and asymptotics for scattering phases