One of the purest examples of self-plagiarism. Accompanied by
several and, from my personal point of view, most disappointing
paradoxes. The first one lies in the easy detection of cheating:
everyone would immediately notice that the last section 5
(Conclusions) practically coincides with the last section 7
(Conclusions) of ref. [41]. The second paradox lies in the
multiplicity of my own role in the story: ref. [41] has been
accepted after my  enthusiastic guest-editor's recommendation. For
this reason, paradoxically, I was able to reveal now the total
failure of the refereeing barriers in Rep. Math. Phys. where neither
the carbon-copied form of the text nor the full coincidence of the
majority of relevant equations have been detected. For getting its
flavor and extent, the reader may check that the ``new" final
sequence of equations (57) - (73) of section 4 strictly coincides
with the ``old" final sequence of equations (54) - (62) concatenated
with another sequence of equations (34) - (39) carbon-copied from
section 4 of ref. [41]. The last but not least paradox is that in
the extended abstract of ref. [41] (written in March 2009 by myself
-- see MR2455812/2009h:81163) I recommended to start reading the
text (published in the special issue of J. Phys. A) from the last
section. Not being aware that after a minor revision and cca one
year later, we shall all be given the second try in Rep. Math. Phys.

MR2591149 Lavagno, A. Basic-deformed quantum mechanics. Rep. Math.
Phys. 64 (2009), no. 1-2, 79--91. 81R50 (33D90 81Q65)

=========on [41]:========

•3. 3. 2009 MR2455812 Lavagno, A. Deformed quantum mechanics and
$q$-Hermitian operators. J. Phys. A: Math. Theor. 41 (2008), no. 24,
244014, 9 pp. 81S05 (39A20 81Q05 81R50) (2009h:81163)

Compact and neat presentation of a fresh idea -- either a proposal
of a new family of Schroedinger equations for quantum theory or a
proposal of a new realization of Hilbert spaces. For accelerated
reading I would recommend skipping all the tutorials and start
reading from the last section 6 which looks like just a summary of
the standard principles of quantum mechanics. Using a slightly
strange notation. The impatient reader is then recommended to search
for definitions in section 5. There, the notation is explained as,
in essence, converting the vector space of wave functions into the
Hilbert space of states. Based on the introduction of a certain
fairly specific and nonstandard inner product called q-deformed
product. Now, the reader understands the point and may return, if
necessary, to section 2 (which explains what is q-calculus and how
one can get the Jackson's representation of q-deformed Heisenberg
algebra) and sections 3 and 4 which recollect some author's older
results on q-deformed Fokker-Planck equation which, via  the
Risken's stochastic quantization, enable him to arrive finally at
the q-deformed Hamiltonian (34).