{"id":112648,"date":"2015-08-11T03:00:00","date_gmt":"2015-08-11T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=88cc435f79126f65d49e7b780ac7ae3c"},"modified":"2015-08-11T03:00:00","modified_gmt":"2015-08-11T00:00:00","slug":"some-problems-in-applications-of-the-linear-variational-method","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=112648","title":{"rendered":"Some problems in applications of the linear variational method"},"content":{"rendered":"<p>The linear variational method is a standard computational method in quantum mechanics and quantum<br \/>\nchemistry. As taught in most classes, the general guidance is to include as many basis functions as<br \/>\npractical in the variational wave function. However, if it is desired to study the patterns of<br \/>\nenergy change accompanying the change of system parameters such as the shape and strength of the<br \/>\npotential energy, the problem becomes more complicated. We use one-dimensional systems with a<br \/>\nparticle in a rectangular or in a harmonic potential confined in an infinite rectangular box to<br \/>\nillustrate situations where a variational calculation can give incorrect results. These situations<br \/>\nresult when the energy of the lowest eigenvalue is strongly dependent on the parameters that<br \/>\ndescribe the shape and strength of the potential. The numerical examples described in this work are<br \/>\nprovided as cautionary notes for practitioners of numerical variational calculations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The linear variational method is a standard computational method in quantum mechanics and quantum<br \/>\nchemistry. As taught in most classes, the general guidance is to include as many basis functions as<br \/>\npractical in the variational wave function. However,&#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-112648","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\/112648","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=112648"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/112648\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=112648"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=112648"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=112648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}