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


SIGMA 5 (2009), 083, 7 pages      arXiv:0908.1755      http://dx.doi.org/10.3842/SIGMA.2009.083
Contribution to the Proceedings of the 5-th Microconference Analytic and Algebraic Methods V

Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty

T.K. Jana a and P. Roy b
a) Department of Mathematics, R.S. Mahavidyalaya, Ghatal 721212, India
b) Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108, India

Received June 30, 2009, in final form August 10, 2009; Published online August 12, 2009

Abstract
We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are η pseudo-Hermitian and the metric operator is found explicitly in both the cases.

Key words: non-Hermitian; minimal length.

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