{"id":290207,"date":"2016-10-06T02:00:00","date_gmt":"2016-10-05T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=cd9a9f3fdbd9b226ed2abf31c6428388"},"modified":"2016-10-06T02:00:00","modified_gmt":"2016-10-05T23:00:00","slug":"fermis-golden-rule-its-derivation-and-breakdown-by-an-ideal-model","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=290207","title":{"rendered":"Fermi\u2019s golden rule: its derivation and breakdown by an ideal model"},"content":{"rendered":"<p>Fermi\u2019s golden rule is of great importance in quantum dynamics. However, in many textbooks on<br \/>\nquantum mechanics, its contents and limitations are obscured by the approximations and arguments in<br \/>\nthe derivation, which are inevitable because of the generic setting considered. Here we propose to<br \/>\nintroduce it by an ideal model, in which the quasi-continuum band consists of equaldistant levels<br \/>\nextending from ##IMG## [http:\/\/ej.iop.org\/images\/0143-0807\/37\/6\/065406\/ejpaa4187ieqn1.gif] {$-\\infty<br \/>\n$} to ##IMG## [http:\/\/ej.iop.org\/images\/0143-0807\/37\/6\/065406\/ejpaa4187ieqn2.gif] {$+\\infty $} , and<br \/>\neach of them couples to the discrete level with the same strength. For this model, the transition<br \/>\nprobability in the first order perturbation approximation can be calculated analytically by invoking<br \/>\nthe Poisson summation formula. It turns out to be a piecewise linear function of time, demonstrating<br \/>\non the one hand the key features of Fermi\u2019s golden&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fermi\u2019s golden rule is of great importance in quantum dynamics. However, in many textbooks on<br \/>\nquantum mechanics, its contents and limitations are obscured by the approximations and arguments in<br \/>\nthe derivation, which are inevitable because of the ge&#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-290207","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\/290207","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=290207"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/290207\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=290207"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=290207"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=290207"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}