{"id":301222,"date":"2016-10-25T02:00:00","date_gmt":"2016-10-24T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=d5f31260a01e2a20e6fe8d73ebf0112f"},"modified":"2016-10-25T02:00:00","modified_gmt":"2016-10-24T23:00:00","slug":"wave-like-variables-of-a-classical-particle-and-their-connections-to-quantum-mechanics","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=301222","title":{"rendered":"Wave-like variables of a classical particle and their connections to quantum mechanics"},"content":{"rendered":"<p>In many texts, the transition from classical mechanics to quantum mechanics is achieved by<br \/>\nsubstituting the action for the phase angle. The paper presents a different approach to show some<br \/>\nconnections between classical and quantum mechanics for a single particle for an audience at<br \/>\ngraduate and postgraduate levels. Firstly, it is shown that a wave equation of action can be derived<br \/>\nunder the free particle condition and the Legendre transform. The wave-like solutions of the action,<br \/>\nHamiltonian and momentum of the free particle are presented. Using the discrete approximation, the<br \/>\nequation of motion of a single particle, in scalar potential field, is obtained in a similar form to<br \/>\nSchr\u00f6dinger\u2019s equation. The rest of the paper discusses the propagation, superposition of the<br \/>\nwave-like dynamic variables and their connections to quantum mechanics. The superposition of the<br \/>\nvariables of a particle is generally distinct from the superposition of classical waves (e.g.<br \/>\nacoustics). The quantum &#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In many texts, the transition from classical mechanics to quantum mechanics is achieved by<br \/>\nsubstituting the action for the phase angle. The paper presents a different approach to show some<br \/>\nconnections between classical and quantum mechanics for a sin&#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-301222","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\/301222","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=301222"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/301222\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=301222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=301222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=301222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}