  We show that and how point interactions offer one of the most suitable guides
towards a quantitative analysis of properties of certain specific non-Hermitian
(usually called PT-symmetric) quantum-mechanical systems. A double-well model
is chosen, an easy solvability of which clarifies the mechanisms of the
unavoided level crossing and of the spontaneous PT-symmetry breaking. The
latter phenomenon takes place at a certain natural boundary of the domain of
the "acceptable" parameters of the model. Within this domain the model mediates
a nice and compact explicit illustration of the not entirely standard
probabilistic interpretation of the physical bound states in the very recently
developed (so called PT symmetric or, in an alternative terminology,
pseudo-Hermitian) new, fairly exciting and very quickly developing branch of
Quantum Mechanics.
