On the determination of potentials without bound state data

DOI10.1016/0377-0427(94)90037-XzbMath0823.65136OpenAlexW1977887872MaRDI QIDQ1891046

William Rundell, Paul E. Sacks

Publication date: 24 October 1995

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(94)90037-x

zbMATH Keywords

\(S\)-matrixpotential recovery algorithmquantum mechanical inverse scattering

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) PDEs in connection with quantum mechanics (35Q40) (S)-matrix theory, etc. in quantum theory (81U20) Applications to the sciences (65Z05)

Related Items

Inverse spectral-scattering problems on the half-line with the knowledge of the potential on a finite interval ⋮ Recovery of a potential from the ratio of reflection and transmission coefficients ⋮ An inverse problem in coupled mode theory ⋮ Determination of the self-adjoint matrix Schrödinger operators without the bound state data ⋮ Certain inverse uniqueness from the quotients of scattering coefficients ⋮ Compactly supported spherically symmetric potentials are uniquely determined by the phase shift of the \(s\)-wave ⋮ On the missing bound state data of inverse spectral-scattering problems on the half-line ⋮ Inverse scattering with partial information on the potential ⋮ Soliton Theory and Hankel Operators ⋮ Inverse scattering problems where the potential is not absolutely continuous on the known interior subinterval

Cites Work

• On the determination of a differential equation from its spectral function
• Reconstruction Techniques for Classical Inverse Sturm-Liouville Problems
• Inverse scattering on the line
• Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation
• Remarks on the Determination of a Central Field of Force from the Elastic Scattering Phase Shifts
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