  For the description of quantum evolution, the use of a manifestly
time-dependent quantum Hamiltonian $\mathfrak{h}(t) =\mathfrak{h}^\dagger(t)$
is shown equivalent to the work with its simplified, time-independent
alternative $G\neq G^\dagger$. A tradeoff analysis is performed recommending
the latter option. The physical unitarity requirement is shown fulfilled in a
suitable ad hoc representation of Hilbert space.
