{"id":104321,"date":"2015-07-15T03:00:00","date_gmt":"2015-07-15T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=05417c252aa9ef5def1ed5fe4306a9e9"},"modified":"2015-07-15T03:00:00","modified_gmt":"2015-07-15T00:00:00","slug":"the-klein-paradox-a-new-treatment","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=104321","title":{"rendered":"The Klein paradox: a new treatment"},"content":{"rendered":"<p>The Dirac equation requires a treatment of the step potential that differs fundamentally from the<br \/>\ntraditional treatment, because the Dirac plane waves, besides momentum and spin, are characterized<br \/>\nby a quantum number with the physical meaning of sign of charge. Since the Hermitean operator<br \/>\ncorresponding to this quantum number does not commute with the step potential, the time displacement<br \/>\nparameter used in the ansatz of the stationary state does not have the physical meaning of energy.<br \/>\nTherefore there are no paradoxal values of the \u2018energy\u2019. The new solution of the Dirac equation with<br \/>\na step potential is obtained. This solution, again, allows for phenomena of the Klein paradox type,<br \/>\nbut in addition it contains a positron amplitude localized at the threshold point of the step<br \/>\npotential.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Dirac equation requires a treatment of the step potential that differs fundamentally from the<br \/>\ntraditional treatment, because the Dirac plane waves, besides momentum and spin, are characterized<br \/>\nby a quantum number with the physical meaning of sign&#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-104321","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\/104321","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=104321"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/104321\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=104321"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=104321"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=104321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}