Sharp exponential bounds on resonances states and width of resonances

DOI10.1016/0196-8858(88)90011-5zbMath0652.47008OpenAlexW2014492474MaRDI QIDQ1107075

Israel Michael Sigal

Publication date: 1988

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0196-8858(88)90011-5

zbMATH Keywords

hydrogen atomexponential boundsgeodesic distancesAgmon-type approachexistence of resonancesgeometrical theory of resonancesinstanton actionsOppenheimer formulaStark resonanceswidth of resonances

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Scattering theory of linear operators (47A40) Miscellaneous applications of functional analysis (46N99)

Related Items (22)

Spectral resonances which become eigenvalues ⋮ Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ Complex absorbing potential method for Stark resonances ⋮ A Time-Independent Approach for the Study of the Spectral Shift Function and an Application to Stark Hamiltonians ⋮ Shape resonances for distortion analytic schrödinger operators ⋮ Geometric theory of Stark resonances in multielectron systems ⋮ Application of spectral deformation to the Vlasov–Poisson system. II. Mathematical results ⋮ Spectral shift function and resonances for non-semi-bounded and Stark Hamiltonians. ⋮ Bender–Wu formula for the Zeeman effect ⋮ Spectral stability under tunneling ⋮ Breit-Wigner formula for the scattering phase in the Stark effect ⋮ The Mourre estimate in the semiclassical limit ⋮ Lower bounds for resonance widths in potential and obstacle scattering ⋮ Stark ladder resonances for small electric fields ⋮ Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ Stark resonances in disordered systems ⋮ Lower bounds on width of Stark resonances in one dimension ⋮ Semiclassical study of shape resonances in the Stark effect ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2 ⋮ Unnamed Item

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