Basics of Quantum Statistics

Abstract

In this chapter we present some basics on the quantum-theoretical description of macroscopic many-particle systems. A detailed disclosure of thermodynamics and quantum statistics is out of reach for this book.¹ Here we will first introduce the concept of a quantum-theoretical ensemble and the so-called statistical operator, or density operator in short, of a many-particle system, and discuss its properties. We will see that with this approach not only can we calculate expectation values of observables, but we are also led to new notions such as entropy. Looking back on the chapter on quantum gases we will discuss in detail the density operator of a canonical ensemble.