On the isospectrality of the scalar energy-dependent Schrodinger problems

Abstract

In this study, we discuss the inverse spectral problem for the energy-dependent Schrodinger 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.