{"id":284954,"date":"2016-09-26T02:00:00","date_gmt":"2016-09-25T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=dd08c78bdd5597491475d7f8abe64f59"},"modified":"2016-09-26T02:00:00","modified_gmt":"2016-09-25T23:00:00","slug":"quantum-classical-correspondence-for-a-particle-in-a-homogeneous-field","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=284954","title":{"rendered":"Quantum\u2013classical correspondence for a particle in a homogeneous field"},"content":{"rendered":"<p>The correspondence principle provides a prescription to connect quantum physics to classical. It<br \/>\nasserts that the physical quantities evaluated quantum mechanically approach their respective<br \/>\nclassical values for large quantum numbers. This has been shown for the pedagogically important<br \/>\ncases of the particle in a box and a harmonic oscillator. However, a particle in a constant field<br \/>\nhas a wave function related to the Airy function and has at best been treated numerically. Employing<br \/>\nenergy eigenstates we obtain the expectation values of the position, the momentum and their moments<br \/>\nupto fourth order, rigorously and without resorting to numerical or graphical techniques. We compare<br \/>\nthem with the corresponding classical values. We also examine the uncertainty product for the<br \/>\nsystem.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The correspondence principle provides a prescription to connect quantum physics to classical. It<br \/>\nasserts that the physical quantities evaluated quantum mechanically approach their respective<br \/>\nclassical values for large quantum numbers. This has been s&#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-284954","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\/284954","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=284954"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/284954\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=284954"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=284954"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=284954"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}