Gel’fand–Levitan equations with comparison measures and comparison potentials

DOI10.1063/1.523970zbMath0428.34019OpenAlexW1994474277MaRDI QIDQ3864831

H. E. Moses

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1063/1.523970

zbMATH Keywords

inverse problemSchrödinger equationspectral measureGelfand-Levitan equation

Mathematics Subject Classification ID

Hamilton's equations (70H05) Inverse problems for PDEs (35R30) Inverse problems involving ordinary differential equations (34A55) Ordinary differential operators (34L99)

Related Items

Fourier type analysis and the marcenko equation ⋮ The use of comparison filters in linear filter theory ⋮ The Gel’fand–Levitan equation on a finite interval ⋮ Exactly solvable models and dynamic quantum systems

Cites Work

• Inverse problem of quantum scattering theory. II
• Korteweg-de Vries equation: a completely integrable Hamiltonian system
• The determination of the scattering potential from the spectral measure function
• The Inverse Problem in the Quantum Theory of Scattering
• A Generalization of the Direct and Inverse Problem for the Radial Schrödinger Equation
• A generalization of the Gel’fand–Levitan equation for the one-dimensional Schrödinger equation
• A variational principle for the Gel’fand–Levitan equation and the Korteweg–de Vries equation
• A simple verification of the Gelfand‐Levitan equation for the three‐dimensional scattering problem
• Certain Explicit Relationships between Phase Shift and Scattering Potential