Composite quantum Coriolis forces

DOI10.3390/MATH11061375arXiv2303.04263MaRDI QIDQ6428761

Miloslav Znojil

Publication date: 7 March 2023

Abstract: The classical Coriolis force finds its quantum analogue in the difference $Sigma(t)=H(t)-G(t)$ where the ``true, observable Hamiltonian $H(t)$ represents the instantaneous energy. The other, ``false Hamiltonian $G(t)$ generates the time-evolution of wave functions. Whenever $Sigma(t)eq0$, quantum mechanics acquires an interaction-picture form. Then, the time-evolution of every observable is generated by the Coriolis operator $Sigma(t)$ ({it alias} ``Heisenberg Hamiltonian) itself. In the paper a sequence of alternative formulae for $Sigma(t)$ is derived under the assumption of an $N-$term factorization of the Dyson-map operator $Omega(t)$ (defined as converting a preselected quasi-Hermitian $H(t)$ into its conventional self-adjoint avatar). It is shown that in the resulting innovative formalism called ``factorization-based non-Hermitian interaction picture (FNIP) one has a choice between $N+1$ alternative forms of the description of quantum dynamics, one of which may prove, for the underlying quantum system, optimal. For illustration, the ``wrong-sign anharmonic oscillator model is recalled.

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