{"id":399438,"date":"2017-04-18T02:00:00","date_gmt":"2017-04-17T23:00:00","guid":{"rendered":"https:\/\/www.fyysika.ee\/?guid=82038168c59cc54f2fd18d29e33b14ae"},"modified":"2017-04-18T02:00:00","modified_gmt":"2017-04-17T23:00:00","slug":"about-the-non-relativistic-limit-of-the-phase-velocity-of-matter-waves-2","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=399438","title":{"rendered":"About the non-relativistic limit of the phase velocity of matter waves"},"content":{"rendered":"<p>This work revisits the apparent paradox that emerges from some results found in many basic textbooks<br \/>\nwhich address the problem of calculating the phase velocity of free particles in the relativistic<br \/>\nregime and its relation with the same quantity in the non-relativistic regime. Because some books<br \/>\nuse the Newtonian kinetic energy and others use the total relativistic energy (including the rest<br \/>\nenergy), the non-relativistic limit of the relativistic phase velocity differs from the Newtonian<br \/>\nphase velocity, which can be confusing for many students. This paper proposes expressing the phase<br \/>\nvelocity by first subtracting the rest energy from the relativistic energy before imposing the usual<br \/>\nde Broglie relations. In addition to providing the corresponding Newtonian phase velocity, it also<br \/>\nprovides a relativistic Schr\u00f6dinger equation which intuitively reduces to the non-relativistic<br \/>\nSchr\u00f6dinger equation in the appropriate regime. The problem of the equivalence between the<br \/>\nrelativistic Sc&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This work revisits the apparent paradox that emerges from some results found in many basic textbooks<br \/>\nwhich address the problem of calculating the phase velocity of free particles in the relativistic<br \/>\nregime and its relation with the same quantity in t&#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-399438","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\/399438","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=399438"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/399438\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=399438"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=399438"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=399438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}