Some properties of the one-dimensional potentials

Abstract

The main aim of this paper is to study the properties of the one-dimensional potentials. In this paper, we have studied the connection between the one-dimensional potentials and the self-adjoint part of the operator L􀀀1 K , which L􀀀1 K is the solution to the one-dimensional Cauchy problem. Moreover, a new method is used that allows us to reduce the spectral problem for the Helmholtz potential to the equivalent problem.