Non-stationary non-Hermitian "wrong-sign'' quantum oscillators and their meaningful physical interpretation

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 Schrödinger-equation generators $G(t)$ but also the Heisenberg-equation generators $\mathrm{\Sigma }(t)$ are phenomenologically irrelevant, with spectra which are, in general, complex. Only the sum $H(t)=G(t)+\mathrm{\Sigma }(t)$ retains the standard physical meaning of instantaneous energy. For illustration, the ``wrong-sign’’ quartic oscillators are recalled and reconsidered.