Quantum Statistics

Abstract

Our rather detailed considerations on Statistical Physics have so far been purely of classical nature. It goes without saying that we would not have any problem to uncover the limits of its validity, i.e., to expose inconsistencies with the experiment, as we have been with the Classical Mechanics. Ultimately, the correct description of nature needs the superordinate Quantum Mechanics. We therefore will have to rewrite the Classical Statistical Physics of the first chapter to a Quantum Statistics. It will turn out thereby that the basic concepts will remain the same, but they will have to be combined, though, with some typical quantum-mechanical aspects. Let us recall once more: Classically the complete description of a physical system is accomplished by the specification of the phase π = (q, p), which changes with time in the phase space according to Hamilton’s equations of motion (1.13) and defines therewith the phase trajectory of the system. Statistical methods become necessary in the case of incomplete information about the initial conditions, which are indispensable for the solution of the equations of motion. Such an incomplete information is the normal case for macroscopic systems.