The Statistics of Composite Systems According to the New Quantum Mechanics / Statistik zusammengesetzter Systeme nach der neueren Quanten-Mechanik

Abstract

1. Only one kind of statistics applies in classical mechanics. In fact the behavior of a system is completely (i. e., also microscopically) determined if the equations of motion are known. The latter does not influence the macroscopic behavior of the system since according to the quasi-ergodic hypothesis, it will get arbitrarily close to any state of the given energy after a long enough time, and statistical mechanics deals with averages when the system goes through all such states many times. We obtain the probability of the macroscopic state of the system according to this classical, or, as it is called, Boltzmann statistics if we calculate the number of ways its various parts can be placed in the phase-space cells compatible with this state. In counting these distributions we must distinguish two states in which the same number of atoms are placed in the same cells but they differ from each other through an interchange of atoms. In combinatorics this rule is expressed by considering the atoms as distinguishable, and we must calculate the number of possible distributions of the atoms in the cells.