Exact Statistical Mechanics of Particle in a box using Canonical Ensemble

R.K. Sathish , K. M. Udayanandan , Augustine. A

Nehru Arts and science College

Statistical mechanics has been used for obtaining thermodynamics of systems mainly with classical energy and rarely for systems with quantum energy. For most of the situations with quantum energy, evaluation of the partition function which involves summation, is done by replacing the summation by integration. This replacement kills the basic effect of quantization like zero point energy and effects like the influence of size. Here we show that Euler-Maclaurin [EM] summation formula can be used to obtain the exact statistical mechanics of particles with discrete energy. We hope this method will help undergraduates for solving, similar problems in statistical mechanics using canonical ensemble.