Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

I will present a picture of Quantum Mechanics based on the geometrical description of physical observables in terms of expectation value functions, generalizing thus the so called Ehrenfest picture of quantum systems. In particular, I will describe the set of pure and mixed states of a quantum system and its geometrical properties. The basic geometrical tools reproduce the algebraic structure of the set of observables on a Hilbert space. This formalism incorporate in a natural way the probabilistic description of Quantum Mechanics. The geometrical formalism allows to analyze from a new perspective the properties of quantum systems, such as dynamical equations, uncertainty relations, coherent states and the non-unitary evolution of open systems. I will focus in the application of the formalism to describe the Markovian evolution of quantum systems determined by the Kossakowski-Lindblad equation.