Numerical Estimation of the Partition Function in Quantum Statistics

A method for estimating the partition function of a quantum mechanical system is described. The method is based on a technique for evaluating the Wiener integrals in terms of which the partition function may be expressed. This technique involves first, an approximation of the Wiener integral by an n...

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Bibliographic Details
Published in:Journal of mathematical physics 1962-11, Vol.3 (6), p.1251-1264
Main Author: Fosdick, Lloyd D.
Format: Article
Language:English
Subjects:
DIFFERENTIAL EQUATIONS
INTERACTIONS
MONTE CARLO METHOD
NUMERICALS
OSCILLATIONS
PARTICLES
PARTITION FUNCTION
PHYSICS
QUANTUM MECHANICS
STATISTICS
WIENER INTEGRALS
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Summary:A method for estimating the partition function of a quantum mechanical system is described. The method is based on a technique for evaluating the Wiener integrals in terms of which the partition function may be expressed. This technique involves first, an approximation of the Wiener integral by an n‐dimensional integral and, second, a Monte Carlo estimation of the value of the n‐dimensional integral. Application of the method to a harmonic oscillator and a pair of interacting particles in a box in two dimensions is described.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1703867