Ideal Quantum Gases

Abstract

Although the noninteracting BE and FD gases are not in themselves suitable representations for their quantum liquid counterparts, the ideal-gas model serves in both instances as a necessary starting point for theoretical investigations of the liquids. An appreciation of the features of the ideal gases is indeed indispensable if we are to attempt an understanding of the real fluids, and for this reason we include here a brief summary of some of the more important properties of ideal BE and FD systems. There are several approaches in statistical mechanics that may be appropriately applied to these problems to achieve essentially the same results. The philosophy and much of the mathematics of these methods will be omitted here but may be found in standard texts of statistical physics [see, for example, Eyring et al. (¹) and Huang(²)]. For the present purposes, it will be convenient to develop simultaneously some preliminary results for the BE and FD systems and then later to distinguish between the two in greater detail. In order to achieve a degree of consistency with at least one standard text, the notation used here will to a large extent follow that of Huang (²). However, the elegant discussion of the BE gas by London (³) ought not to be overlooked.