{"id":399638,"date":"2017-04-20T02:00:00","date_gmt":"2017-04-19T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=17e49def041d42ba6f89aa8f8aa593dd"},"modified":"2017-04-20T02:00:00","modified_gmt":"2017-04-19T23:00:00","slug":"quantum-and-classical-limits-in-a-potential-step","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=399638","title":{"rendered":"Quantum and classical limits in a potential step"},"content":{"rendered":"<p>We have often found among many of our students and colleagues the common idea that the mathematical<br \/>\nexpression for a physical quantity that is essentially of quantum nature must contain a dependence<br \/>\non \u210f. Conversely, a phenomenon described by classical physics should contain no explicit reference<br \/>\nto \u210f. However, the problem of a particle encountering a discontinuous potential step, which is one<br \/>\nof the simplest examples in quantum mechanics, contradicts this common thought: even when the<br \/>\nparticle carries enough kinetic energy to go across the step, the resulting expression for the<br \/>\nreflection probability is non-zero\u2014a purely quantum phenomenon\u2014and yet it contains no reference to<br \/>\n\u210f. We show that the absence of \u210f in this purely quantum expression is due to the idealised limit in<br \/>\nwhich the potential rises sharply at a single position, thus losing any reference to a length<br \/>\ndimension in the problem. To address the correct classical limit of the phenomenon we first<br \/>\nregularise the discont&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We have often found among many of our students and colleagues the common idea that the mathematical<br \/>\nexpression for a physical quantity that is essentially of quantum nature must contain a dependence<br \/>\non \u210f. Conversely, a phenomenon described by class&#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-399638","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\/399638","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=399638"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/399638\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=399638"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=399638"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=399638"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}