Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 007, 24 pages      arXiv:0901.2916      http://dx.doi.org/10.3842/SIGMA.2009.007
Contribution to the Proceedings of the VIIth Workshop ''Quantum Physics with Non-Hermitian Operators''

On the Spectrum of a Discrete Non-Hermitian Quantum System

Ebru Ergun
Department of Physics, Ankara University, 06100 Tandogan, Ankara, Turkey

Received October 28, 2008, in final form January 13, 2009; Published online January 19, 2009

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.

Key words: difference operator; non-Hermiticity; spectrum; eigenvalue; eigenvector; completely continuous operator.

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