Composite quantum Coriolis forces

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 $\Sigma (t)\ne 0$, 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.

28 pp

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Cited by in corpus (1)

• Three alternative model-building strategies using quasi-Hermitian time-dependent observables