A simple way of approximating the canonical partition functions in statistical mechanics

We propose a simple pedagogical way of introducing the Euler-MacLaurin summation formula in an undergraduate course on statistical mechanics. The reason is that the students may feel more comfortable and confident if they are able to deduce the main equations. To this end we put forward two alternat...

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Autor principal: Fernández, Francisco Marcelo
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2015
Materias:
Química
Euler-maclaurin formula
Partition function
Simpler approach
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/101444
https://ri.conicet.gov.ar/11336/48844
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-101444
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Química
Euler-maclaurin formula
Partition function
Simpler approach
spellingShingle Química
Euler-maclaurin formula
Partition function
Simpler approach
Fernández, Francisco Marcelo
A simple way of approximating the canonical partition functions in statistical mechanics
topic_facet Química
Euler-maclaurin formula
Partition function
Simpler approach
description We propose a simple pedagogical way of introducing the Euler-MacLaurin summation formula in an undergraduate course on statistical mechanics. The reason is that the students may feel more comfortable and confident if they are able to deduce the main equations. To this end we put forward two alternative routes: the first one is the simplest and yields the first two terms of the expansion. The second one is somewhat more elaborate and takes into account all the correction terms. We apply both to the calculation of the simplest one-particle canonical partition functions for the translational, vibrational and rotational degrees of freedom. The more elaborate, systematic calculation of the correction terms is suitable for motivating the students to explore the possibility of using available computer algebra software that enable one to avoid long and tedious manipulation of algebraic equations.
format Articulo
Preprint
author Fernández, Francisco Marcelo
author_facet Fernández, Francisco Marcelo
author_sort Fernández, Francisco Marcelo
title A simple way of approximating the canonical partition functions in statistical mechanics
title_short A simple way of approximating the canonical partition functions in statistical mechanics
title_full A simple way of approximating the canonical partition functions in statistical mechanics
title_fullStr A simple way of approximating the canonical partition functions in statistical mechanics
title_full_unstemmed A simple way of approximating the canonical partition functions in statistical mechanics
title_sort simple way of approximating the canonical partition functions in statistical mechanics
publishDate 2015
url http://sedici.unlp.edu.ar/handle/10915/101444
https://ri.conicet.gov.ar/11336/48844
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