{"id":88811,"date":"2015-05-13T03:00:00","date_gmt":"2015-05-13T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=e0b7605fcd89b5915c35fadae8b5ad86"},"modified":"2015-05-13T03:00:00","modified_gmt":"2015-05-13T00:00:00","slug":"numerical-determination-of-the-eigenenergies-of-the-schrdinger-equation-in-one-dimension","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=88811","title":{"rendered":"Numerical determination of the eigenenergies of the Schr?dinger equation in one dimension"},"content":{"rendered":"<p>In most approaches to teaching quantum mechanics, discrete energy levels are introduced through the<br \/>\nexample of the infinite square well. Here, the boundary conditions at the walls, namely a vanishing<br \/>\namplitude of the wave function, lead to quantized energy levels. This contribution extends the<br \/>\ndiscussion to more realistic, smooth potentials in one dimension, including non-symmetric<br \/>\npotentials. A numerical solution algorithm for the corresponding time-independent Schr?dinger<br \/>\nequation illustrates quantization in an intuitive manner by use of simple forward-shooting and<br \/>\nbisection methods. It also demonstrates how computational physics can go beyond finding approximate<br \/>\nsolutions to a specific problem and truly aid the understanding of a basic concept in physics.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In most approaches to teaching quantum mechanics, discrete energy levels are introduced through the<br \/>\nexample of the infinite square well. Here, the boundary conditions at the walls, namely a vanishing<br \/>\namplitude of the wave function, lead to quantized &#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-88811","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\/88811","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=88811"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/88811\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=88811"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=88811"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=88811"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}