{"id":360066,"date":"2017-02-03T03:00:00","date_gmt":"2017-02-03T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=78a93e6986295ceb37984a0b51a491fb"},"modified":"2017-02-03T03:00:00","modified_gmt":"2017-02-03T00:00:00","slug":"quantum-harmonic-oscillator-an-elementary-derivation-of-the-energy-spectrum","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=360066","title":{"rendered":"Quantum harmonic oscillator: an elementary derivation of the energy spectrum"},"content":{"rendered":"<p>An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of<br \/>\nlinear differential equation theory or Fourier analysis are required, but rather only a few basics<br \/>\nof elementary calculus. The pivotal role in our analysis is played by the sole particle localization<br \/>\nconstraint, which implies square integrability of stationary-state wavefunctions. The oscillator<br \/>\nground-state characterization is then achieved in a way that could be grasped, in principle, even by<br \/>\nfirst-year undergraduates. A very elementary approach to build up and to characterize all<br \/>\nhigher-level energy eigenstates completes our analysis.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of<br \/>\nlinear differential equation theory or Fourier analysis are required, but rather only a few basics<br \/>\nof elementary calculus. The pivotal role in our analys&#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-360066","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\/360066","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=360066"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/360066\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=360066"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=360066"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=360066"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}