{"id":608055,"date":"2017-10-24T02:00:00","date_gmt":"2017-10-23T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=bca77944b5ddee826eb47eca5c6c7c5e"},"modified":"2017-10-24T02:00:00","modified_gmt":"2017-10-23T23:00:00","slug":"the-equally-spaced-energy-levels-of-the-quantum-harmonic-oscillator-revisited-a-back-to-frontreconstruction-of-an-n-body-hamiltonian","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=608055","title":{"rendered":"The equally spaced energy levels of the quantum harmonic oscillator revisited: a back-to-front\r\nreconstruction of an n -body Hamiltonian"},"content":{"rendered":"<p>The \u2018back-to-front\u2019 derivation of the properties of the quantum harmonic oscillator (QHO), starting<br \/>\nwith its equally spaced energy levels, is re-examined. A new derivation that exploits the natural<br \/>\nrotational symmetry of the QHO is proposed. The new approach allows the \u2018back-to-front\u2019 idea to be<br \/>\nextended further by showing that it is possible to derive the Hamiltonian of a system of particles<br \/>\nfrom the starting point that the population is represented by a natural number. This involves the<br \/>\nsymmetry properties of phasors and Schwinger&#8217;s theory of angular momentum. The analysis is also<br \/>\nextended to multi-mode bosonic systems and fermionic systems. It is suggested that these results<br \/>\noffer an alternative way to formulate physics, based on discreteness.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The \u2018back-to-front\u2019 derivation of the properties of the quantum harmonic oscillator (QHO), starting<br \/>\nwith its equally spaced energy levels, is re-examined. A new derivation that exploits the natural<br \/>\nrotational symmetry of the QHO is proposed. The new &#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-608055","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\/608055","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=608055"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/608055\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=608055"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=608055"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=608055"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}