A heuristic analysis of correspondence between classical and
quantum mechanics for the class of dynamical models where
quantization requires the use of a non-standard scalar product. In
a way supported by an explicitly solvable illustrative example the
author emphasizes the important role of semi-classical analysis in
a systematic clarification of the puzzles presented by the so
called PT-symmetric potentials which are complex but which are
able to generate bound states with real energies in a certain
domain of parameters. The text summarizes the talk presented
during the 3rd International Workshop ``Pseudo-Hermitian
Hamiltonians in Quantum Physics" (Istanbul, Turkey, June 2005).

MR2230233 Ahmed, Zafar Phase space trajectories and quantization
in PT-symmetric quantum mechanics. Czechoslovak J. Phys. 55
(2005), no. 9, 1055--1062. 81Q10