On the isospectrality of the scalar energy-dependent Schrödingerproblems

Authors

TÜBA GÜLŞEN
ETIBAR SADI PANAKHOV

DOI

10.3906/mat-1612-71

Abstract

In this study, we discuss the inverse spectral problem for the energy-dependent Schrödinger equation on a finite interval. We construct an isospectrality problem and obtain some relations between constants in boundary conditions of the problems that constitute isospectrality. Above all, we obtain degeneracy of $ K(x,t)-K_{0}{ (x,t)}$ and $L(x,t)-L_{0} (x,t)$ by using a different approach. Some of the main results of our study coincide with results reported by Jodeit and Levitan. However, the method to obtain degeneracy is completely different. Furthermore, we consider all above results for the nonisospectral case.

Keywords

Energy-dependent Schrödinger equation, isospectrality problem, Gelfand-Levitan equation

First Page

139

Last Page

154

Recommended Citation

GÜLŞEN, TÜBA and PANAKHOV, ETIBAR SADI (2018) "On the isospectrality of the scalar energy-dependent Schrödingerproblems," Turkish Journal of Mathematics: Vol. 42: No. 1, Article 13. https://doi.org/10.3906/mat-1612-71
Available at: https://journals.tubitak.gov.tr/math/vol42/iss1/13