{"id":112654,"date":"2015-08-11T03:00:00","date_gmt":"2015-08-11T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=1aced734b9e948bc8d59e3b4602ca514"},"modified":"2015-08-11T03:00:00","modified_gmt":"2015-08-11T00:00:00","slug":"a-note-on-the-fermi-energy-of-an-ideal-fermi-gas-trapped-under-a-generic-power-law-potential-in-d-dimension","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=112654","title":{"rendered":"A note on the Fermi energy of an ideal Fermi gas trapped under a generic power law potential in d\r\n-dimension"},"content":{"rendered":"<p>The average energy per fermion in the case of a Fermi gas with any kinematic characteristic, trapped<br \/>\nunder the most general power law potential in d -dimension has been calculated at zero temperature.<br \/>\nIn a previous paper (Acharyya M 2010 Eur. J Phys. 31 [http:\/\/dx.doi.org\/10.1088\/0143-0807\/31\/6\/L01]<br \/>\nL89 ) it was shown, in the case of a free ideal Fermi gas, as the dimension increases the average<br \/>\nenergy approaches the Fermi energy and in infinite dimension the average energy becomes equal to the<br \/>\nFermi energy at T = 0. In this letter it is shown that, for a trapped system at finite dimension the<br \/>\naverage energy depends on a power law exponent, but as the dimension tends to infinity the average<br \/>\nenergy coincides with the Fermi energy for any power law exponent. The result obtained in this<br \/>\nmanuscript is more general, as we can describe the free system as well as any trapped system with an<br \/>\nappropriate choice of power law exponent, and is true for an&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The average energy per fermion in the case of a Fermi gas with any kinematic characteristic, trapped<br \/>\nunder the most general power law potential in d -dimension has been calculated at zero temperature.<br \/>\nIn a previous paper (Acharyya M 2010 Eur. J Phys&#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-112654","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\/112654","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=112654"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/112654\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=112654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=112654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=112654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}