Quantum Models

Quantum effects are important when matter is dense and the temperature is low. These are two distinct, albeit interrelated, effects. The first is the effect of quantum statistics. The second effect is a purely dynamic effect, that is, related to the displacement of the particles in the medium. This chapter presents the hydrodynamic approach because its generalization to quantum mechanics is quite simple. It also presents the quantum generalization of kinetic theory that requires the predefinition of a certain number of concepts. The hydrodynamic representation of Schrödinger's equation is actually almost as old as Schrödinger's equation itself. The Wigner distribution represents a form of probability of a quantum system in phase space. A representation of quantum mechanics in the phase space requires calculation of the mean values of observables, which must be represented by functions of the variables of the phase space, namely the position and the momentum.