Classical and Quantum Systems: Alternative Hamiltonian Descriptions
G. Marmo, G. Scolarici, A. Simoni, F. Ventriglia
TL;DR
This paper explores the extension of bi-Hamiltonian and compatible Hermitian structures from classical to quantum systems, providing a new framework for understanding quantum dynamics.
Contribution
It introduces the concept of bi-Hamiltonian descriptions and compatible Hermitian structures in quantum systems, paralleling classical mechanics.
Findings
Bi-Hamiltonian descriptions are possible for quantum systems.
Compatible Hermitian structures can be defined analogously to classical Poisson structures.
The framework bridges classical and quantum Hamiltonian formalisms.
Abstract
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson structures.
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