Non-Stationary Non-Hermitian “Wrong-Sign” Quantum Oscillators and Their Meaningful Physical Interpretation

In the framework of quantum mechanics using quasi-Hermitian operators the standard unitary evolution of a non-stationary but still closed quantum system is only properly described in the non-Hermitian interaction picture (NIP). In this formulation of the theory both the states and the observables vary with time. A few aspects of implementation of this picture are illustrated via the “wrong-sign” quartic oscillators. It is shown that in contrast to the widespread belief, both of the related Schrödinger-equation generators [Formula: see text] and the Heisenberg-equation generators [Formula: see text] are just auxiliary concepts. Their spectra are phenomenologically irrelevant and, in general, complex. It is argued that only the sum [Formula: see text] of the latter operators retains the standard physical meaning of the instantaneous energy of the unitary quantum system in question.