Levinson’s theorem, zero-energy resonances, and time delay in one-dimensional scattering systems

DOI10.1063/1.530481zbMath0807.35120OpenAlexW2140824557MaRDI QIDQ4314248

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Publication date: 7 December 1994

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

Full work available at URL: https://doi.org/10.1063/1.530481

zbMATH Keywords

Schrödinger equationenergy behaviordouble-potential system

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) (2)-body potential quantum scattering theory (81U05)

Related Items (13)

Scattering state of Klein-Gordon particles by \(q\)-parameter hyperbolic Poschl-Teller potential ⋮ Scattering in one dimension: The coupled Schrödinger equation, threshold behaviour and Levinson’s theorem ⋮ Scattering and transmission resonances in one-dimensional Hulthén potential barrier ⋮ On the number of states bound by one-dimensional finite periodic potentials ⋮ A note on one-loop soliton quantum mass corrections ⋮ A supersymmetric exotic field theory in (1+1) dimensions: one loop soliton quantum mass corrections ⋮ Quantum temporal probabilities in tunneling systems ⋮ Theorem of Levinson via the spectral density ⋮ Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions ⋮ On the number of bound states for the one-dimensional Schrödinger equation ⋮ Dynamical formulation of low-energy scattering in one dimension ⋮ Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances ⋮ Scattering of a spinless particle by an asymmetric Hulthén potential within the effective mass formalism

Cites Work

• Inverse scattering by a local impurity in a periodic potential in one dimension
• Remarks on inverse scattering in one dimension
• Analytic Properties of Radial Wave Functions
• Inverse scattering. I. One dimension
• A factorization of the scattering matrix for the Schrödinger equation and for the wave equation in one dimension
• Inverse scattering on the line

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