The Phase Space Model of Nonrelativistic Quantum Mechanics

Abstract

We focus on several questions arising during the modelling of quantum systems on a phase space. First, we discuss the choice of phase space and its structure. We include an interesting case of discrete phase space. Then, we introduce the respective algebras of functions containing quantum observables. We also consider the possibility of performing strict calculations and indicate cases where only formal considerations can be performed. We analyse alternative realisations of strict and formal calculi, which are determined by different kernels. Finally, two classes of Wigner functions as representations of states are investigated.

Dynamical entropic measure of nonclassicality of phase-dependent family of Schrödinger cat states

“…The application of space-phase methods to the study of quantum systems initiated by Wigner allows looking at the theory of these systems as the statistical theory in which observables characterizing them form a non-commutative algebra 1 – 3 . This observation is the cornerstone of the space-phase formulation of quantum theory and has given the impulse to develop more rigorous rudiments of this approach 4 – 8 . As a result of these studies, quantum mechanics emerged as a deformation of the symplectic structures characteristic of classical mechanics formulated in the phase-space language.…”