Classical Representations of Quantum Mechanics Related to Statistically Complete Observables
Abstract
Description
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding is the existence of so-called statistically complete observables and the duality between the state spaces and the spaces of the observables, the latter holding in the quantum as well as in the classical case. In the phase-space context, we further discuss joint position-momentum observables, Hilbert spaces of infinitely differentiable functions on phase space, and dequantizations. Finally, the relation of quantum dynamics to the classical Liouville dynamics is investigated.
118 pages, no figures. This work was published 1997 as a book by Wissenschaft und Technik Verlag Berlin. Since it has proved to be of interest to some researchers, it is published here for an easier access
118 pages, no figures. This work was published 1997 as a book by Wissenschaft und Technik Verlag Berlin. Since it has proved to be of interest to some researchers, it is published here for an easier access