{"id":225640,"date":"2016-05-27T02:00:00","date_gmt":"2016-05-26T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=8dc1a52cd882e39b19992a4c5649bff6"},"modified":"2016-05-27T02:00:00","modified_gmt":"2016-05-26T23:00:00","slug":"bound-state-eigenfunctions-need-to-vanish-faster-than-imghttpej-iop-orgimages0143-0807374045404toc_ejpaa2747ieqn1-gif-x-32","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=225640","title":{"rendered":"Bound state eigenfunctions need to vanish faster than ##IMG##\r\n[http:\/\/ej.iop.org\/images\/0143-0807\/37\/4\/045404\/toc_ejpaa2747ieqn1.gif] {$| x{| }^{-3\/2}$}"},"content":{"rendered":"<p>In quantum mechanics, students are taught to practice that the eigenfunction of a physical bound<br \/>\nstate must be continuous and vanishing asymptotically so that it is normalizable in ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/37\/4\/045404\/ejpaa2747ieqn3.gif] {$xin (-infty ,infty )$} .<br \/>\nHere we caution that such states may also give rise to infinite uncertainty in the position ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/37\/4\/045404\/ejpaa2747ieqn4.gif] {$({rm{Delta }}x=infty )$} ,<br \/>\nwhereas ##IMG## [http:\/\/ej.iop.org\/images\/0143-0807\/37\/4\/045404\/ejpaa2747ieqn5.gif] {${rm{Delta<br \/>\n}}p$} remains finite. Such states may be called loosely bound and spatially extended states, and may<br \/>\nbe avoided by an additional condition that the eigenfunction vanishes asymptotically faster than<br \/>\n##IMG## [http:\/\/ej.iop.org\/images\/0143-0807\/37\/4\/045404\/ejpaa2747ieqn6.gif] {$| x{| }^{-3\/2}$} .<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In quantum mechanics, students are taught to practice that the eigenfunction of a physical bound<br \/>\nstate must be continuous and vanishing asymptotically so that it is normalizable in ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/37\/4\/045404\/ejpaa2747ieqn&#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-225640","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\/225640","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=225640"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/225640\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=225640"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=225640"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=225640"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}