  Quantum mechanics of closed, unitary quantum systems can be formulated in
non-Hermitian interaction picture (NIP) in which both the states and the
observables vary with time. Then, in general, not only the
Schr\"{o}dinger-equation generators $G(t)$ but also the Heisenberg-equation
generators $\Sigma(t)$ are phenomenologically irrelevant, with spectra which
are, in general, complex. Only the sum $H(t)=G(t)+\Sigma(t)$ retains the
standard physical meaning of instantaneous energy. For illustration, the
``wrong-sign'' quartic oscillators are recalled and reconsidered.
