Within the applied Quantum Theory the majority of phenomenological
models is constructed in Hilbert space where the metric operator
$\Theta$ (which enables us to define the scalar product, the space
of functionals and the norms of elements) is trivial, $\Theta =
I$. Although it has been known for a long time that the theory
might also be built on quasi-Hermitian Hamiltonians (i.e.,
Hamiltonians which are essentially self-adjoint with respect to
some nontrivial metric operator $\Theta \neq I$), the practical
constructive implementation of the idea has only been initiated by
the recent discovery of models (i.e., ``natural" candidates for
quasi-Hermiticity) with real spectra of $H \neq H^\dagger$. Under
the trademark of the so called PT-symmetry, this new direction of
research became quite fashionable recently, and the letter in
question (which summarizes briefly also a part of the broader
context) contributes significantly to its further development by
promoting a new idea of working with time-dependent models. A
solvable example (with prospective applicability in quantum optics
and, perhaps, quantum chemistry) is presented and described in
some detail.

MR2169996 de Souza Dutra, A. ; Hott, M. B. ; dos Santos, V. G. C.
S. Time-dependent non-Hermitian Hamiltonians with real energies.
Europhys. Lett. 71 (2005), no. 2, 166--171.