Scattering in one dimension: The coupled Schrödinger equation, threshold behaviour and Levinson’s theorem

DOI10.1063/1.531762zbMath0867.34072arXivquant-ph/9608032OpenAlexW3123844547MaRDI QIDQ5284674

W. van Dijk, K. A. Kiers

Publication date: 22 January 1997

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

Full work available at URL: https://arxiv.org/abs/quant-ph/9608032

zbMATH Keywords

scattering amplitudesbound statesLevinson's theoremhalf-bound statesthreshold behaviourcoupled Schrödinger equationscattering in one dimension

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items

Scattering properties for a pair of Schrödinger type operators on cylindrical domains ⋮ On bound states for systems of weakly coupled Schrödinger equations in one space dimension ⋮ Factorization of the transition matrix for the general Jacobi system ⋮ Theorem of Levinson via the spectral density ⋮ Quantum tunneling in an exactly solvable double-barrier potential: barrier transmission near the zero energy ⋮ Spectral properties at a threshold for two-channel Hamiltonians. II: Applications to scattering theory ⋮ Vacuum polarization energy for general backgrounds in one space dimension

Cites Work

• Inverse scattering by a local impurity in a periodic potential in one dimension
• Remarks on inverse scattering in one dimension
• The construction of potentials from theS-matrix for systems of differential equations
• Analytic Properties of Radial Wave Functions
• Non-uniqueness in the one-dimensional inverse scattering problem
• Inverse scattering. I. One dimension
• A factorization of the scattering matrix for the Schrödinger equation and for the wave equation in one dimension
• Levinson’s theorem, zero-energy resonances, and time delay in one-dimensional scattering systems
• On the number of states bound by one-dimensional finite periodic potentials
• Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation