On the isospectrality of the scalar energy-dependent Schrödinger problems

Authors: TÜBA GÜLŞEN, ETIBAR SADI PANAKHOV

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

Full Text: PDF