Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-02-01
Annals Phys. 313 (2004) 110-146
Physics
High Energy Physics
High Energy Physics - Theory
34 pages, Latex file
Scientific paper
10.1016/j.aop.2004.03.008
We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a formula for the momentum correlations of arbitrary order and derive explicit expressions for the wavefunctions in terms of time dependent and independent Wigner functions. We show that the pure state quantum condition is preserved by the Moyal (but not by the classical Liouville) time evolution and is consistent with a generic stargenvalue equation. As a by-product Baker's converse construction is generalized both to an arbitrary stargenvalue equation, associated to a generic phase space symbol, as well as to the time dependent case. These results are properly extended to the mixed state quantum condition, which is proved to imply the Heisenberg uncertainty relations. Globally, this formalism yields the complete characterization of the kinematical structure of Wigner quantum mechanics. The previous results are then succinctly generalized for various quasi-distributions. Finally, the formalism is illustrated through the simple examples of the harmonic oscillator and the free Gaussian wave packet. As a by-product, we obtain in the former example an integral representation of the Hermite polynomials.
Dias Nuno Costa
Prata Joao Nuno
No associations
LandOfFree
Admissible states in quantum phase space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Admissible states in quantum phase space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Admissible states in quantum phase space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-627679