Perturbation theory for shape resonances and large barrier potentials

DOI10.1007/BF01976039zbMath0494.34044MaRDI QIDQ1169080

Mark S. Ashbaugh, Evans M. II. Harrell

Publication date: 1982

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

zbMATH Keywords

eigenvaluesresonanceshape resonancesone- dimensional Schrödinger equationlarge barrier potentials

Mathematics Subject Classification ID

Perturbation theories for operators and differential equations in quantum theory (81Q15) Asymptotic properties of solutions to ordinary differential equations (34D05) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential operators (34L99)

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Markov's theorem for weight functions on the unit circle, Truncated Gamow functions, \(\alpha\)-decay and the exponential law, The shape resonance, Sharp exponential bounds on resonances states and width of resonances, Shape resonances for distortion analytic schrödinger operators, Trapping and cascading of eigenvalues in the large coupling limit, New channels of scattering for three-body quantum systems with long-range potentials, Barrier Resonances in Strong Magnetic Fields, Unnamed Item, Unnamed Item, Spectral stability under tunneling, Tunneling resonances in systems without a classical trapping, The Kirkwood–Buckingham variational method and the boundary value problems for the molecular Schrödinger equation, Widths of highly excited shape resonances, Potentials Producing Maximally Sharp Resonances, On a formula of Thompson and McEnteggert for the adjugate matrix, Structural isomers, double wells, resonances, and Dirichlet decoupling, Estimation of the imaginary part of the scattering matrix pole for the three-dimensional Schrödinger equation with a trap potential, Théorie spectrale de quelques variétés à bouts, General lower bounds for resonances in one dimension, An Improved Stability Result for Resonances, Optimal bounds on the fundamental spectral gap with single-well potentials

Cites Work

• Decoupling by a projection
• The mathematical theory of resonances whose widths are exponentially small
• The band-structure of a one-dimensional, periodic system in a scaling limit
• Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory
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