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.

arXiv comment28 pp

References in corpus (24)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Pseudo-Hermitian Representation of Quantum Mechanics
• Biorthogonal Quantum Mechanics
• Pseudospectra in non-Hermitian quantum mechanics
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Time-dependent version of cryptohermitian quantum theory
• On the metric operator for the imaginary cubic oscillator
• Unitary quantum evolution for time-dependent quasi-Hermitian systems with non-observable Hamiltonians
• Three-Hilbert-Space Formulation of Quantum Mechanics
• Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism
• Non-Hermitian interaction representation and its use in relativistic quantum mechanics
• Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
• Non-Hermitian Heisenberg representation
• The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics
• Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation
• Repeatability of measurements: Equivalence of hermitian and non-hermitian observables
• Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
• Time-dependent metric for the two dimensional, non-Hermitian coupled oscillator
• Hybrid form of quantum theory with non-Hermitian Hamiltonians
• Systematics of quasi-Hermitian representations of non-Hermitian quantum models
• Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• The Coriolis Effect Further Described in the Seventeenth Century

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