A more or less routine continuation and marginal extension of the
older, nicer paper [17] by the same authors. The initial idea of
both of these short studies is very promising, suggesting several
versions of a non-commutative extension of 2D isotropic harmonic
oscillator. Almost immediately, a strong disappointment comes not
only with the rather elementary form of results and with their
presentation which is, at many points, misleading, but also with a
purely formal essence of the message. In the language of physics the
deeper sense of the recent introduction of PT symmetry (lying in the
``improbable" reality of the spectra) is completely ignored (i.a.,
the authors report, without any particular explanations, that the
spectra are, in general, not real). Last Section 4 inspired by
Nanayakkara’s paper [18] is appended adding a few extremely trivial
(viz., first-order) perturbative results on an anisotropic perturbed
generalization of the previous examples. The meaning of this
addendum is also questionable (one expects that the higher-order
corrections will almost certainly complexify the energies).
Summarizing, a quickly produced paper representing an almost fully
wasted opportunity.
MR2485771 Giri, Pulak Ranjan; Roy, P. Non-Hermitian quantum
mechanics in non-commutative space. Eur. Phys. J. C Part. Fields 60
(2009), no. 1, 157--161. 81Rxx