A new treatment of macroscopic observables in quantum mechanics

A procedure is developed to obtain a joint probability distribution for a set of noncommuting observables. On one side this procedure is a generalization of methods of statistical thermodynamics, on the other one it is linked to Ludwig's generalization of the axiomatics of quantum mechanics. The Gaussian approximation of our probability distribution has expectation values and correlation functions coinciding with those of usual quantum statistical mechanics. A remarkable feature of our formalism is that completely deterministic situations can arise in a quite natural way. As an example the ideal gas is discussed with particular reference to the Bose-Einstein condensation.