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


SIGMA 5 (2009), 089, 2 pages      arXiv:0908.2341      http://dx.doi.org/10.3842/SIGMA.2009.089
Contribution to the Proceedings of the 5-th Microconference Analytic and Algebraic Methods V

Comment on ''Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty''

Bijan Bagchi a and Andreas Fring b
a) Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009, India
b) Centre for Mathematical Science, City University London, Northampton Square, London EC1V 0HB, UK

Received August 18, 2009; Published online September 17, 2009

Abstract
We demonstrate that the recent paper by Jana and Roy entitled ''Non-Hermitian quantum mechanics with minimal length uncertainty'' [SIGMA 5 (2009), 083, 7 pages, arXiv:0908.1755] contains various misconceptions. We compare with an analysis on the same topic carried out previously in our manuscript [arXiv:0907.5354]. In particular, we show that the metric operators computed for the deformed non-Hermitian Swanson models differs in both cases and is inconsistent in the former.

Key words: non-Hermitian Hamiltonians; deformed canonical commutation relations; minimal length.

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References

  1. Bagchi B., Fring A., Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems, arXiv:0907.5354.
  2. Jana T.K., Roy P., Non-Hermitian quantum mechanics with minimal length uncertainty, SIGMA 5 (2009), 083, 7 pages, arXiv:0908.1755.

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