IJPAM: Volume 109, No. 2 (2016)

ON A COMPATIBILITY RELATION BETWEEN
THE MAXWELL-BOLTZMANN AND
THE QUANTUM DESCRIPTION OF A GAS PARTICLE

Eugen Grycko$^1$, Werner Kirsch$^2$, Tobias Mühlenbruch$^3$
$^{1,2,3}$Department of Mathematics and Computer Science
University of Hagen
Universitätsstrasse 1
D-58084 Hagen, GERMANY


Abstract. We consider a quantum particle at a thermal equilibrium and compute its Gibbs state. The transition to the thermodynamic limit reveals that the asymptotic quantum variance of the velocity operator of the particle coincides with the Maxwell-Boltzmann variance of the velocity distribution, which means that the Maxwell-Boltzmann description of the ideal gas is in some sense compatible with the quantum description of a gas in a macroscopic container at an arbitrary temperature.

Received: April 25, 2016

AMS Subject Classification: 81V99, 83B30, 83B31

Key Words and Phrases: Hamiltonian, quantum Gibbs state, thermodynamic limit

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DOI: 10.12732/ijpam.v109i2.20 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 2
Pages: 469 - 476


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