Inverse spectral problem for the Schrödinger equation with an additional linear potential

DOI10.1134/S0040577920010067zbMath1445.81018OpenAlexW3013030476MaRDI QIDQ2193670

M. G. Makhmudova, Agil K. Khanmamedov

Publication date: 20 August 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577920010067

zbMATH Keywords

Schrödinger equationAiry functionGelfand-Levitan equationinverse scattering problemtransformation operatoradditional linear potential

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) 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)

Related Items (3)

The Riemann function of the Cauchy problem for a second-order hyperbolic equation with a growing coefficient ⋮ SCATTERING PROBLEM OF THE PERTURBED AIRY EQUATION ON A HALF-AXIS ⋮ The Dirichlet problem for perturbed Stark operators in the half-line

Cites Work

• Inverse scattering problem for one-dimensional Schrödinger operators related to the general Stark effect
• The method of transformation operators in the inverse scattering problem. The one-dimensional 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
• THE DIRECT AND INVERSE SCATTERING PROBLEMS FOR THE ONE-DIMENSIONAL PERTURBED HILL OPERATOR
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