
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 NonHermitian Operators''
On the Spectrum of a Discrete NonHermitian 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 nonHermitian 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; nonHermiticity; spectrum; eigenvalue; eigenvector; completely continuous operator.
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