The Quantum‐Mechanical Equation of State

1950 ◽  
Vol 18 (10) ◽  
pp. 1412-1413 ◽  
Author(s):  
Robert W. Zwanzig
Keyword(s):  
Equation Of State ◽  
Quantum Mechanical ◽  
Mechanical Equation

The perfect Bose-Einstein gas in the theory of the quantum-mechanical grand canonical ensembles

1952 ◽  
Vol 212 (1111) ◽  
pp. 552-558 ◽  
Keyword(s):  
Equation Of State ◽  
Energy Levels ◽  
Einstein Condensation ◽  
Quantum Mechanical ◽  
Condensation Phenomenon ◽  
Bose Einstein ◽  
Canonical Ensembles ◽  
Grand Canonical ◽  
Different Parts ◽  
Number Of Particles

The theory of quantum-mechanical grand canonical ensembles is used to derive for the case of a perfect Bose-Einstein gas the average number of particles in the different energy levels, the fluctuations in these numbers and the equation of state. The Einstein condensation phenomenon is then discussed, and it is shown that in a p-v diagram (v being the specific volume) the isotherm consists of two analytically different parts in the limit where the number of particles in the system, JV, goes to infinity. It is also shown that for finite N at the critical volume ∂ n p/∂v n is of the order N1/3 (n-2) in accordance with a result obtained by Wergeland & Hove-Storhoug.

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