Basic Quantum Statistical Mechanics
2.1 ELEMENTARY STATISTICAL MECHANICS
If a system in equilibrium can be in any of N states, then the probability of the system having energy is given by , where the partition function Z is defined by 
Here, is a Boltzmann constant, and T is a temperature. For quantum mechanical system of states , where denotes the state with energy , the expected value of the quantum mechanical operator A is defined by
This fundamental law is the essence of statistical mechanics, with the concept of thermal equilibrium and temperature. If a system is very weakly coupled to a heat bath at a given temperature, if the coupling is indefinite or not known ...