# Chapter 6: Many-Particle Systems

We apply the techniques of statistical mechanics to many particle systems. Our focus will be on systems where we can treat the particles as noninteracting. The first half of the chapter discusses classical and semiclassical systems, and the second half discusses systems where quantum mechanics is essential.

The key results of classical systems are the Maxwell velocity and speed distributions and the equipartition theorem, which are valid for gases, liquids, and solids.

Quantum systems that are discussed include blackbody radiation (considered as a collection of photons), the Debye model of solids (considering quantized sound waves or normal modes as phonons), Fermi systems such as electrons in metals, neutron stars, and white dwarfs, and Bose gases which can condense into a single ground state at low enough temperatures. To study these systems we use the grand canonical ensemble to treat the indistinguishability of the particles, and introduce the concepts of single particle density of states and the mean occupation of each single particle state (distribution function) at a temperature $T$ and chemical potential $\mu$.

## Programs

- Program 6.1: Lennard-Jones MD
- Program 6.2: Quantum Gas Integral
- Program 6.3: Bose Gas Sum