Symmetry of bound and antibound states in the semiclassical limit for a general class of potentials

DOI10.1090/S0002-9939-2010-10519-1zbMath1206.34106arXiv0911.4282OpenAlexW3104838754MaRDI QIDQ4929989

Subhroshekhar Ghosh, Semyon Dyatlov

Publication date: 27 September 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.4282

zbMATH Keywords

Schrödinger operatorbound statesNeumann eigenvaluesantibound states

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) (S)-matrix theory, etc. in quantum theory (81U20) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (2)

On the resonances and eigenvalues for a 1D half-crystal with localised impurity ⋮ Mathematical study of scattering resonances

Uses Software

• ARPACK

Cites Work

• Asymptotics of resonances for a Schrödinger operator with vector values
• Symmetry of bound and antibound states in the semiclassical limit
• On the location of resonances for Schrödinger operators in the semiclassical limit. I: Resonances free domains
• Distribution of poles for scattering on the real line
• Asymptotic distribution of resonances in one dimension
• Resonances in one dimension and Fredholm determinants
• Bounds on scattering poles in one dimension
• Bounds on complex eigenvalues and resonances
• Analytic properties of the scattering matrix
• Inverse resonance scattering on the real line

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