The needs of the applied quantum physics (say, in the domain of 
atomic nuclei) currently motivate studies of non-local models. On 
an elementary level the paper combines ``theoretical" 
non-localities (caused by the use of a nonstandard definition of 
the inner product in Hilbert space as necessary, i.a., in the so
called PT-symmetric models) with the ``pragmatic" non-local 
choice of the interaction. Ccomments are formulated on the 
underlying mathematics as well as physics, emphasizing the 
puzzling manifest violation of the unitarity or of the 
``handedness", as well as, by citing the results of Ahmed [6], on 
the possible role of the separability of interactions. In the 
choice of the kinematics (of a mere one-dimensional scattering of 
a single particle) and of the dynamics (mediated by an elementary 
separable potential a la Yamaguchi), just the first steps are 
being made.  Still, within their analytically solvable exercise 
the authors are able to ask important questions, most of which 
are left without any widely accepted answer at present. 


MR2257374 Cannata, Francesco; Ventura, Alberto Scattering by
$\scr{PT}$-symmetric non-local potentials. Czechoslovak J. Phys. 
56 (2006), no. 9, 943--951. 81Q10 (81Uxx)