Composite quantum Coriolis forces
- URL: http://arxiv.org/abs/2303.04263v1
- Date: Tue, 7 Mar 2023 22:18:20 GMT
- Title: Composite quantum Coriolis forces
- Authors: Miloslav Znojil
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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 $\Sigma(t)\neq 0$,
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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