The exactly solvable models like  square well potential and/or its
delta-function limiting case offer a lot of insight in the generic
structure and character of bound and scattering states in quantum
mechanics. In the letter the authors ask what happens with these
models when you move beyond the framework of the latter physical
theory and weaken the usual Hermiticity of the observables to their
mere parity-pseudohermiticity. In an innovative, investigative and
necessarily incomplete manner, the authors link the parity-violating
terms in the potentials with their traditional physical sink/source
meaning. First of all,  they offer the explicit description of the
scattering states. Two pictures illustrate the situation, opening new
questions rather than answering too many of the old ones. The
parallel study of the PT-symmetry breaking for bound states seems
less exciting because it merely reproduces some older results (cf.,
e.g., ref. [31] or the study of the spontaneous breakdown of PT
symmetry in the solvable square-well model by M. Znojil and G. Levai
in Mod. Phys. Lett. A16 (2001) 2273-2280, hep-th/0111213). Still, as
a whole the text represents a valid contribution to the recent
intensive development of the subject as summarized recently during
the 1st International Workshop ``Pseudo-Hermitian Hamiltonians in
Quantum Physics", with the proceedings to appear in Czechoslovak J.
Physics, vol. 54, 2004, as its January issue.


MR1976165 Narayan Deb, Ram ; Khare, Avinash ; Dutta Roy, Binayak .
Complex optical potentials and pseudo-Hermitian Hamiltonians. Phys.
Lett. A 307 (2003), no. 4, 215--221.