{"id":263118,"date":"2016-08-17T02:00:00","date_gmt":"2016-08-16T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=ad8eea35016078be96d04728ea573df6"},"modified":"2016-08-17T02:00:00","modified_gmt":"2016-08-16T23:00:00","slug":"generators-of-dynamical-symmetries-and-the-correct-gauge-transformation-in-the-landau-level-problemuse-of-pseudomomentum-and-pseudo-angular-momentum","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=263118","title":{"rendered":"Generators of dynamical symmetries and the correct gauge transformation in the Landau level problem:\r\nuse of pseudomomentum and pseudo-angular momentum"},"content":{"rendered":"<p>Due to the importance of gauge symmetry in all fields of physics, and motivated by an article<br \/>\nwritten almost three decades ago that warns against a naive handling of gauge transformations in the<br \/>\nLandau level problem (a quantum electron moving in a spatially uniform magnetic field), we point out<br \/>\na proper use of the generators of dynamical symmetries combined with gauge transformation methods to<br \/>\neasily obtain exact analytical solutions for all Landau level-wavefunctions in arbitrary gauge. Our<br \/>\nmethod is different from the old argument and provides solutions in an easier manner and in a<br \/>\nbroader set of geometries and gauges; in so doing, it eliminates the need for extra procedures (i.e.<br \/>\na change of basis) pointed out as a necessary step in the old literature, and gives back the<br \/>\nstandard simple result, provided that an appropriate use is made of the dynamical symmetries of the<br \/>\nsystem and their generators. In this way the present work will at least be useful for<br \/>\nuniversity-level educa&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Due to the importance of gauge symmetry in all fields of physics, and motivated by an article<br \/>\nwritten almost three decades ago that warns against a naive handling of gauge transformations in the<br \/>\nLandau level problem (a quantum electron moving in a sp&#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-263118","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\/263118","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=263118"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/263118\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=263118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=263118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=263118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}