The Density Matrix and Partition Function in Quantum Statistical Mechanics

2003 ◽  
pp. 307-315
Author(s):  
Floyd Williams
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Density Matrix ◽  
Quantum Statistical Mechanics ◽  
Quantum Statistical

Theory of Unimolecular Decomposition— The Statistical Approach

1996 ◽  
Author(s):  
Tomas Baer ◽  
William L. Hase
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Density Of States ◽  
Quantum Statistical Mechanics ◽  
Thermodynamic Quantities ◽  
Unimolecular Decomposition ◽  
Thermal Systems ◽  
System P ◽  
Quantum Statistical ◽  
Basic Ideas

The partition function and the sum or density of states are functions which are to statistical mechanics what the wave function is to quantum mechanics. Once they are known, all of the thermodynamic quantities of interest can be calculated. It is instructive to compare these two functions because they are closely related. Both provide a measure of the number of states in a system. The partition function is a quantity that is appropriate for thermal systems at a given temperature (canonical ensemble), whereas the sum and density of states are equivalent functions for systems at constant energy (microcanonical ensemble). In order to lay the groundwork for an understanding of these two functions as well as a number of other topics in the theory of unimolecular reactions, it is essential to review some basic ideas from classical and quantum statistical mechanics. As discussed in chapter 2, the classical Hamiltonian, H(p,q), is the total energy of the system expressed in terms of the momenta (p) and positions (q) of the atoms in the system.

INTEGRAL REPRESENTATION FOR THE GR AND PARTITION FUNCTION IN QUANTUM STATISTICAL MECHANICS OF EXCLUSION STATISTICS

2000 ◽  
Vol 14 (05) ◽  
pp. 485-506 ◽  
Author(s):  
KAZUMOTO IGUCHI ◽  
KAZUHIKO AOMOTO
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Integral Representation ◽  
Quantum Statistical Mechanics ◽  
Ideal Gas ◽  
Alternative Proof ◽  
Quantum Statistical

We derive an exact integral representation for the gr and partition function for an ideal gas with exclusion statistics. Using this we show how the Wu's equation for the exclusion statistics appears in the problem. This can be an alternative proof for the Wu's equation. We also discuss that singularities are related to the existence of a phase transition of the system.

On N. N. Bogolyubov's works in classical and quantum statistical mechanics

1993 ◽  
Vol 45 (2) ◽  
pp. 171-214
Author(s):  
Yu. A. Mitropolskii ◽  
D. Ya. Petrina
Keyword(s):  
Statistical Mechanics ◽  
Quantum Statistical Mechanics ◽  
Quantum Statistical
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