In the context of model-building in quantum mechanics, the paper
offers a neat sample of the power and subtlety of the replacement
of brute-force analytic calculations (like explicit
differentiations of polynomials) by the search for the underlying
algebraic structures (like commutation relations). Using this
philosophy the authors feel inspired by the Swanson's
modified-oscillator model and by its deeper analyses (cf. refs.
[16] and [17], respectively). They show that and how a mere
reinterpretation of the creation and annihilation operators
broadens perceivably the class of the models. The emergence of a
new solvable quantum non-Hermitian model with the Rosen-Morse-type
bound states is described in detail for illustration. In a
marginal comment let us add that a very similar idea and method
were also proposed and used by C. Quesne in ref. [18] (the
reference can now be updated: J. Phys. A: Math. Theor. 40 (2007)
F745). It is worth noticing that although ref. [18] was published
a month earlier in the same Journal, both of these papers have
precisely the same date of submission of the MS to the Journal's
editorial office (viz., 22 May 2007). This is remarkable
coincidence which is purely incidental because the respective
choices of the direction of the application of the idea are
entirely different.


MR2371139 Sinha, A.; Roy, P. Generalized Swanson models and their
solutions. J. Phys. A 40 (2007), no. 34, 10599--10610. 81Q10