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

• URL: http://arxiv.org/abs/2304.07103v1
• Date: Fri, 14 Apr 2023 12:52:15 GMT
• Title: Non-stationary non-Hermitian "wrong-sign'' quantum oscillators and their meaningful physical interpretation
• Authors: Miloslav Znojil
• Abstract summary: Quantum mechanics of closed, unitary quantum systems can be formulated in non-Hermitian interaction picture. Only the sum $H(t)=G(t)+Sigma(t)$ retains the standard physical meaning of instantaneous energy.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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