Quantum Statistical Mechanics of a Many-Body System with Several Components

1963 ◽  
Vol 129 (2) ◽  
pp. 944-959 ◽  
Author(s):  
R. K. Pathria ◽  
M. P. Kawatra
Keyword(s):  
Statistical Mechanics ◽  
Quantum Statistical Mechanics ◽  
Body System ◽  
Many Body ◽  
Quantum Statistical

Quantum Ensembles

2019 ◽  
pp. 285-296
Author(s):  
Robert H. Swendsen
Keyword(s):  
Statistical Mechanics ◽  
Probability Distributions ◽  
Quantum Statistical Mechanics ◽  
Stationary States ◽  
Mechanical State ◽  
Many Body ◽  
Model Probability ◽  
Exact Position ◽  
Quantum Statistical ◽  
Many Body Systems

The study of quantum statistical mechanics begins with a review of the basic principles of quantum mechanics. Schrödinger’s equation is introduced and Eigenstates (or stationary states) are defined. Model probability for quantum statistics is assumed to have a uniform distribution in phases. Wave functions for many-body systems are defined. The density matrix is introduced. The Planck entropy and the microcanonical ensemble are defined. The differences between classical and quantum statistical mechanics are all based on the differing concepts of a microscopic ‘state’. While the classical microscopic state (specified by a point in phase space) determines the exact position and momentum of every particle, the quantum mechanical state determines neither; quantum states can only provide probability distributions for observable quantities.

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