Inverse scattering by a local impurity in a periodic potential in one dimension

DOI10.1063/1.525968zbMath0524.34026OpenAlexW4254163043MaRDI QIDQ3037810

Roger G. Newton

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1063/1.525968

zbMATH Keywords

Riemann-Hilbert problemSchrödinger equationinverse scatteringHill's equationBloch functionsLevinson's theoremBloch solutionsscattering by impurities

Mathematics Subject Classification ID

(2)-body potential quantum scattering theory (81U05) Inverse problems involving ordinary differential equations (34A55) Ordinary differential operators (34L99)

Related Items

Scattering in one dimension: The coupled Schrödinger equation, threshold behaviour and Levinson’s theorem, Scattering theory for mesoscopic quantum systems with non-trivial spatial asymptotics in one dimension, Scattering for step-periodic potentials in one dimension, Levinson’s theorem, zero-energy resonances, and time delay in one-dimensional scattering systems, Remarks on inverse scattering in one dimension, Continuity of the S matrix for the perturbed Hill’s equation, Theorem of Levinson via the spectral density, Unnamed Item, Inverse scattering by a local impurity in a periodic potential in one dimension. II, Inverse scattering theory for one-dimensional Schrödinger operators with steplike finite-gap potentials, Coupling constant thresholds of perturbed periodic Hamiltonians, The inverse scattering problem for a perturbed difference Hill equation, Transition matrix of point interactions as the scaling limit of integrable potentials on the real line

Cites Work

• The spectrum of Hill's equation
• Inverse scattering. I. One dimension
• Inverse scattering on the line
• On a generalized Hilbert problem