Bound states and inverse scattering for the Schrödinger equation in one dimension

DOI10.1063/1.530671zbMath0822.34070OpenAlexW2029300491MaRDI QIDQ4837124

Tuncay Aktosun

Publication date: 4 July 1995

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

Full work available at URL: https://doi.org/10.1063/1.530671

zbMATH Keywords

potentialone-dimensional Schrödinger equationnorming constantsbound state energies

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Inverse scattering problems in quantum theory (81U40) Inverse problems involving ordinary differential equations (34A55)

Related Items (10)

Integral equation methods for the inverse problem with discontinuous wave speed ⋮ Potential splitting and numerical solution of the inverse scattering problem on the line ⋮ Recovery of a potential from the ratio of reflection and transmission coefficients ⋮ An inverse problem in coupled mode theory ⋮ Factorization for the Full-Line Matrix Schrödinger Equation and a Unitary Transformation to the Half-Line Scattering ⋮ Inverse scattering with partial information on the potential ⋮ Inverse problems for selfadjoint Schrödinger operators on the half line with compactly supported potentials ⋮ Computational methods for some inverse scattering problems ⋮ Inverse scattering problems where the potential is not absolutely continuous on the known interior subinterval ⋮ Inverse phaseless scattering on the line with partial information

Cites Work

• Explicit Wiener-Hopf factorization for certain non-rational matrix functions
• On the Riemann–Hilbert problem for the one-dimensional Schrödinger equation
• 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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