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

  • Agil K. Khanmamedov EMAIL logo and Nigar F. Gafarova
Published/Copyright: July 16, 2020

Abstract

An anharmonic oscillator T ( q ) = - d 2 d x 2 + x 2 + q ( x ) on the half-axis 0 x < 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.

MSC 2010: 34A55; 34B24

Acknowledgements

The authors thank the referee for the useful comments which helped improve the contents of the paper.

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Received: 2019-12-12
Revised: 2020-01-20
Accepted: 2020-03-23
Published Online: 2020-07-16
Published in Print: 2021-10-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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