{"id":331778,"date":"2016-12-06T03:00:00","date_gmt":"2016-12-06T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=27bc247ace5dcae31861b6ca89e085ba"},"modified":"2016-12-06T03:00:00","modified_gmt":"2016-12-06T00:00:00","slug":"semiconductor-quantum-wells-with-bendaniel-duke-boundary-conditions-approximate-analytical-results","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=331778","title":{"rendered":"Semiconductor quantum wells with BenDaniel\u2013Duke boundary conditions: approximate analytical results"},"content":{"rendered":"<p>The Schr\u00f6dinger equation for a particle moving in a square well potential with BenDaniel\u2013Duke<br \/>\nboundary conditions is solved. Using algebraic approximations for trigonometric functions, the<br \/>\ntranscendental equations of the bound states energy are transformed into tractable, algebraic<br \/>\nequations. For the ground state and the first excited state, they are cubic equations; we obtain<br \/>\nsimple formulas for their physically interesting roots. The case of higher excited states is also<br \/>\nanalysed. Our results have direct applications in the physics of type I and type II semiconductor<br \/>\nheterostructures.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Schr\u00f6dinger equation for a particle moving in a square well potential with BenDaniel\u2013Duke<br \/>\nboundary conditions is solved. Using algebraic approximations for trigonometric functions, the<br \/>\ntranscendental equations of the bound states energy are tr&#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-331778","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\/331778","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=331778"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/331778\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=331778"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=331778"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=331778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}