The relationship between the single particle partition function and volume (V) is established through the localization of particles. When particles are nonlocalized, the single particle partition function is directly proportional to V, as described in Pathria's "Statistical Mechanics," chapter 4, section 4.4, equations 2 and 14. In contrast, when particles are localized, the partition function becomes independent of V, since the particles are confined to specific locations. This distinction arises from the quantum mechanical treatment of particles as wave functions, where the number of antinodes, indicative of possible locations, is influenced by the volume of the system.
PREREQUISITESPhysicists, graduate students in statistical mechanics, and researchers exploring quantum systems and their thermodynamic properties will benefit from this discussion.