Towards a tomographic representation of quantum mechanics on the plane

Abstract

On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In this representation the average values of observables can be calculated by means of integration over all the plane.

arXiv comment11 pages, accepted for publication in the Topical Issue of Physica Scripta: 150 years of Margarita and Vladimir Man'ko