On the transformation operator for the Schrödinger equation with an additional linear potential

DOI10.1134/S0016266320010116zbMath1447.81110OpenAlexW3081909891MaRDI QIDQ2199014

M. G. Makhmudova, Agil K. Khanmamedov

Publication date: 16 September 2020

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0016266320010116

zbMATH Keywords

inverse problemSchrödinger equationAiry functiontransformation operatoradditional linear potential

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) Inverse scattering problems in quantum theory (81U40) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Inverse problems involving ordinary differential equations (34A55) Linear integral equations (45A05)

Related Items (2)

Transformation operator for the Schrödinger equation with additional exponential potential ⋮ Unnamed Item

Cites Work

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• Inverse scattering problem for one-dimensional Schrödinger operators related to the general Stark effect
• Spectral and scattering theory of Schrödinger operators related to the Stark effect
• Asymptotics of resonances for 1D Stark operators
• Resonances for 1D Stark operators
• Inverse scattering problem for the Schrödinger equation with an additional quadratic potential on the entire axis
• Spectral properties of the complex Airy operator on the half-line
• Inverse problem for harmonic oscillator perturbed by potential, characterization
• A Riemann–Hilbert approach to the inverse problem for the Stark operator on the line

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