Exactly solvable models have a particular appeal in Quantum 
Mechanics where there are not that many of them. One of the 
traditional purposes of their study is pragmatic (typically, in 
perturbation teory), another one, apparently pursued in paper in 
question, is exporative and pedagogical. The author picks up two 
popular models of a particle confined in a particular (viz., 
``scarf") one-dimensional potential and compares the properties 
of the bound states generated by their standard versions 
(manifestly self-adjoint in the Dirac's sense) and 
``PT-symmetric" versions (self-adjoint with respect to a less 
trivial, non-local and ad hoc constructed scalar product). Amply 
the author employs the fact that the model is solvable in terms 
of the Gauss' hypergeometric functions. This paves the way 
towards a detection of the presence/absence of the so called 
quasi-parity quantum number, of the so called 
PT-symmetry-breaking couplings at which the energies acquire  
imaginary components, etc.

MR2257375 Lévai, G. Comparative analysis of real and 
$\scr{PT}$-symmetric Scarf potentials. Czechoslovak J. Phys. 56 
(2006), no. 9, 953--966. 81Q10