{"id":167692,"date":"2016-01-08T03:00:00","date_gmt":"2016-01-08T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=c979d2c69f28ab2aef4d4255ab1de35f"},"modified":"2016-01-08T03:00:00","modified_gmt":"2016-01-08T00:00:00","slug":"effects-of-the-generalised-uncertainty-principle-on-quantum-tunnelling","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=167692","title":{"rendered":"Effects of the generalised uncertainty principle on quantum tunnelling"},"content":{"rendered":"<p>In a previous paper (Blado et al 2014 Eur. J. Phys. 35<br \/>\n[http:\/\/dx.doi.org\/10.1088\/0143-0807\/35\/6\/065011] 065011 ), we showed that quantum gravity effects<br \/>\ncan be discussed with only a background in non-relativistic quantum mechanics at the undergraduate<br \/>\nlevel by looking at the effect of the generalised uncertainty principle (GUP) on the finite and<br \/>\ninfinite square wells. In this paper, we derive the GUP corrections to the tunnelling probability of<br \/>\nsimple quantum mechanical systems which are accessible to undergraduates (alpha decay, simple models<br \/>\nof quantum cosmogenesis and gravitational tunnelling radiation) and which employ the WKB<br \/>\napproximation, a topic discussed in undergraduate quantum mechanics classes. It is shown that the<br \/>\nGUP correction increases the tunnelling probability in each of the examples discussed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In a previous paper (Blado et al 2014 Eur. J. Phys. 35<br \/>\n[http:\/\/dx.doi.org\/10.1088\/0143-0807\/35\/6\/065011] 065011 ), we showed that quantum gravity effects<br \/>\ncan be discussed with only a background in non-relativistic quantum mechanics at the undergradua&#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-167692","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\/167692","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=167692"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/167692\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=167692"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=167692"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=167692"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}