On the absence of resonances for Schrödinger operators with non- trapping potentials in the classical limit

DOI10.1007/BF01207259zbMath0651.47007MaRDI QIDQ1106440

Markus Klein

Publication date: 1986

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Schrödinger operatorsrescalingpolar coordinatesshape resonance problempredissociationbound for the resolvent of a dilated Schrödinger operator associated with an exterior scalingDirichlet condition on the boundarynon-trapping energy

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) General theory of partial differential operators (47F05) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (10)

The shape resonance ⋮ On the mathematical theory of predissociation ⋮ Shape resonances for distortion analytic schrödinger operators ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Geometric bounds on the density of resonances for semiclassical problems ⋮ The Mourre estimate in the semiclassical limit ⋮ Stark ladder resonances for small electric fields ⋮ A note on the absence of resonances for Schrödinger operators ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Opérateurs conjugués et propriétés de propagation
• Exterior complex scaling and the AC-Stark effect in a Coulomb field
• Convergent expansions for tunneling
• The shape resonance
• On the mathematical theory of predissociation
• Absence of singular continuous spectrum for certain self-adjoint operators
• A class of analytic perturbations for one-body Schrödinger Hamiltonians

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