{"id":405602,"date":"2017-05-08T02:00:00","date_gmt":"2017-05-07T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=f183d91422fb8bb300fd12585084799b"},"modified":"2017-05-08T02:00:00","modified_gmt":"2017-05-07T23:00:00","slug":"investigating-and-improving-student-understanding-of-the-expectation-values-of-observables-inquantum-mechanics","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=405602","title":{"rendered":"Investigating and improving student understanding of the expectation values of observables in\r\nquantum mechanics"},"content":{"rendered":"<p>The expectation value of an observable is an important concept in quantum mechanics since<br \/>\nmeasurement outcomes are, in general, probabilistic and we only have information about the<br \/>\nprobability distribution of measurement outcomes in a given quantum state of a system. However, we<br \/>\nfind that upper-level undergraduate and PhD students in physics have both conceptual and procedural<br \/>\ndifficulties when determining the expectation value of a physical observable in a given quantum<br \/>\nstate in terms of the eigenstates and eigenvalues of the corresponding operator, especially when<br \/>\nusing Dirac notation. Here we first describe the difficulties that these students have with<br \/>\ndetermining the expectation value of an observable in Dirac notation. We then discuss how the<br \/>\ndifficulties found via student responses to written surveys and individual interviews were used as a<br \/>\nguide in the development of a quantum interactive learning tutorial (QuILT) to help students develop<br \/>\na good grasp of the expectation &#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The expectation value of an observable is an important concept in quantum mechanics since<br \/>\nmeasurement outcomes are, in general, probabilistic and we only have information about the<br \/>\nprobability distribution of measurement outcomes in a given quantum 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-405602","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\/405602","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=405602"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/405602\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=405602"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=405602"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=405602"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}