6Indistinguishable Particles
This chapter introduces the concept of indistinguishability of particles. Although we have neglected it in the preceding chapters, the partition function must be calculated, taking into account the indistinguishability, if the particles of the system are indistinguishable.
First, we learn the concept of indistinguishability in Section 6.1. The next section describes how to express the partition function of a system consisting of N indistinguishable particles using a single‐particle partition function. The expression is effective under a certain condition, which we examine in Section 6.3. Sections 6.4 and 6.5 look at ramifications of the indistinguishability. In the last section, we consider an open system of gas molecules using the concept of indistinguishability.
6.1 Distinguishable Particles and Indistinguishable Particles
So far, we have assumed, without explicitly stating, that all the particles are distinguishable and therefore can be numbered or labeled. It is as if each particle has its own face. Obviously, however, oxygen molecules are not distinguishable. Unlike humans (or animals), the molecules are not distinguishable unless their structures are different.
The particle may be an atom, a molecule, an electron, a wave, or a phonon. Table 6.1 lists examples of distinguishable particles and indistinguishable particles. For distinguishable particles, how to distinguish them is also described. Figure 6.1a shows molecules in a solid state and ...