{"id":110086,"date":"2015-08-04T03:00:00","date_gmt":"2015-08-04T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=2893f59b9649c50330295f2706d63019"},"modified":"2015-08-04T03:00:00","modified_gmt":"2015-08-04T00:00:00","slug":"a-simple-way-of-approximating-the-canonical-partition-functions-in-statistical-mechanics","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=110086","title":{"rendered":"A simple way of approximating the canonical partition functions in statistical mechanics"},"content":{"rendered":"<p>We propose a simple pedagogical way of introducing the Euler\u2013MacLaurin summation formula in an<br \/>\nundergraduate course on statistical mechanics. The reason is that the students may feel more<br \/>\ncomfortable and confident if they are able to deduce the main equations. To this end we put forward<br \/>\ntwo alternative routes: the first one is the simplest and yields the first two terms of the<br \/>\nexpansion. The second one is somewhat more elaborate and takes into account all the correction<br \/>\nterms. We apply both to the calculation of the simplest one-particle canonical partition functions<br \/>\nfor the translational, vibrational and rotational degrees of freedom. The more elaborate, systematic<br \/>\ncalculation of the correction terms is suitable for motivating the students to explore the<br \/>\npossibility of using available computer algebra software that enable one to avoid long and tedious<br \/>\nmanipulation of algebraic equations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We propose a simple pedagogical way of introducing the Euler\u2013MacLaurin summation formula in an<br \/>\nundergraduate course on statistical mechanics. The reason is that the students may feel more<br \/>\ncomfortable and confident if they are able to deduce the mai&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-110086","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/110086","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=110086"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/110086\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=110086"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=110086"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=110086"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}