Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition-Reference-Cited by-同舟云学术

Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition

Published:2020-07-16 Issue:5 Volume:29 Page:675-688
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Khanmamedov Agil K.¹,Gafarova Nigar F.²

Affiliation:

1. Baku State University , AZ 1148 , Baku ; and Institute of Mathematics and Mechanics of the Azerbaijan National Academy of Sciences, AZ 1141, Baku; and Azerbaijan University, AZ 1007, Baku , Azerbaijan

2. Azerbaijan University , AZ 1007 , Baku , Azerbaijan

Abstract

Abstract An anharmonic oscillator T ⁢ ( q ) = - d 2 d ⁢ x 2 + x 2 + q ⁢ ( x )

{T(q)=-\frac{d^{2}}{dx^{2}}+x^{2}+q(x)}

on the half-axis 0 ≤ x < ∞

{0\leq x<\infty}

with the Neumann boundary condition is considered. By means of transformation operators, the direct and inverse spectral problems are studied. We obtain the main integral equations of the inverse problem and prove that the main equation is uniquely solvable. An effective algorithm for reconstruction of perturbed potential is indicated.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2019-0102/pdf

Reference26 articles.

1. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Funcions with Formulas, Graphs, and Mathematical Tables, Natl. Bur. Stand. Appl. Math. Ser. 55, U.S. Government Printing Office, Washington, 1964.

2. S. M. Bagirova and A. K. Khanmamedov, The inverse spectral problem for the perturbed harmonic oscillator on the entire axis, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 44 (2018), no. 2, 285–294.

3. F. A. Berezin and M. A. Shubin, The Schrödinger Equation, Math. Appl. (Sov. Ser.) 66, Kluwer Academic Publishers, Dordrecht, 1991.

4. D. Chelkak, P. Kargaev and E. Korotyaev, An inverse problem for an harmonic oscillator perturbed by potential: Uniqueness, Lett. Math. Phys. 64 (2003), no. 1, 7–21.

5. D. Chelkak, P. Kargaev and E. Korotyaev, Inverse problem for harmonic oscillator perturbed by potential, characterization, Comm. Math. Phys. 249 (2004), no. 1, 133–196.