On the location of resonances for Schrödinger operators in the semiclassical limit. I: Resonances free domains
From MaRDI portal
Publication:1093878
DOI10.1016/0022-247X(87)90077-1zbMath0629.47043OpenAlexW1967669467MaRDI QIDQ1093878
Jean-Michel Combes, Pierre Duclos, Philippe Briet
Publication date: 1987
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0022-247x(87)90077-1
Schrödinger operatorsemi-classical regimelocation of resonancesnon-trapping conditionsthresholds or barrier topsVirial relation
Spectrum, resolvent (47A10) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10)
Related Items
Semiclassical resolvent estimates for the barrier top energy, The shape resonance, Trapped rays in cylindrically symmetric media and poles of the analytically continued resolvent, Sharp exponential bounds on resonances states and width of resonances, Shape resonances for distortion analytic schrödinger operators, Geometric theory of Stark resonances in multielectron systems, Lower bounds on the width of Stark-Wannier type resonances, Semiclassical resolvent estimates for two and three–body schrödinger operators, Application of spectral deformation to the Vlasov–Poisson system. II. Mathematical results, Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances, Semiclassical asymptotic distribution of resonances created by homoclinic and heteroclinic trajectories, Unnamed Item, Geometric bounds on the density of resonances for semiclassical problems, Spectral stability under tunneling, The Mourre estimate in the semiclassical limit, Unnamed Item, Lower bounds for resonance widths in potential and obstacle scattering, Resonances for a semi-classical Schrödinger operator near a non trapping energy level, Stark ladder resonances for small electric fields, Semiclassical resonances generated by crossings of classical trajectories, Resonances in a box, Space-time picture of semiclassical resonances, Open quantum dots: Resonances from perturbed symmetry and bound states in strong magnetic fields, Symmetry of bound and antibound states in the semiclassical limit for a general class of potentials, A note on the absence of resonances for Schrödinger operators, Resonances in the two-center Coulomb systems, The problem of two fixed centers: bifurcation diagram for positive energies, Unnamed Item, Unnamed Item, Unnamed Item
Cites Work
- Exterior complex scaling and the AC-Stark effect in a Coulomb field
- Krein's formula and one-dimensional multiple-well
- The shape resonance
- Absence of high energy resonances for many-body Schrödinger operators
- Absence of singular continuous spectrum for certain self-adjoint operators
- Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions
- A class of analytic perturbations for one-body Schrödinger Hamiltonians
- On the location of the resonances for schrodinger
- Semi-classical bounds for resolvents of schrödinger operators and asymptotics for scattering phases
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
