  The overall principles of what is now widely known as PT-symmetric quantum
mechanics are listed, explained and illustrated via a few examples. In
particular, models based on an elementary local interaction V(x) are discussed
as motivated by the naturally emergent possibility of an efficient
regularization of an otherwise unacceptable presence of a strongly singular
repulsive core in the origin. The emphasis is put on the constructive aspects
of the models. Besides the overall outline of the formalism we show how the
low-lying energies of bound states may be found in closed form in certain
dynamical regimes. Finally, once these energies are found real we explain that
in spite of a manifest non-Hermiticity of the Hamiltonian the time-evolution of
the system becomes unitary in a properly amended physical Hilbert space.
