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

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