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Engineering Quantum Mechanics by Seoung-Hwan Park, Doyeol Ahn

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2

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 c02ue001 is given by c02ue002, where the partition function Z is defined by [1]

(2.1) c02e001

Here, c02ue003 is a Boltzmann constant, and T is a temperature. For quantum mechanical system of states c02ue004, where c02ue005 denotes the state with energy c02ue006, the expected value of the quantum mechanical operator A is defined by

(2.2) c02e002

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 ...

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