On the Spectrum of a Discrete Non-Hermitian Quantum System

Abstract

In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum are established.

Keywords

• difference operator
• non-Hermiticity
• spectrum
• eigenvalue
• eigenvector
• completely continuous operator