The Ehrenfest picture and the geometry of Quantum Mechanics

Abstract

In this paper we develop a picture of Quantum Mechanics based on the description of physical observables in terms of expectation value functions, generalizing thus the so called Ehrenfest theorems for quantum dynamics. Our basic technical ingredient is the set of tools which has been developed in the last years for the geometrical formulation of Quantum Mechanics. In the new picture, we analyze the problem of the dynamical equations, the uncertainty relations and interference and illustrate the construction with the simple case of a two-level system.

Amsart, 17 pages. This paper is based on some lectures delivered by one of us (G. M.) at the international conference "Mathematical Structures in Quantum Systems and applications (MSQS2012)'' which took place at Benasque (Spain), July 8-14, 2012