{"id":247469,"date":"2016-07-20T02:00:00","date_gmt":"2016-07-19T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=6a726e09558fef80d0173fa1c34a7c0f"},"modified":"2016-07-20T02:00:00","modified_gmt":"2016-07-19T23:00:00","slug":"applying-classical-geometry-intuition-to-quantum-spin","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=247469","title":{"rendered":"Applying classical geometry intuition to quantum spin"},"content":{"rendered":"<p>Using concepts of geometric orthogonality and linear independence, we logically deduce the form of<br \/>\nthe Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of<br \/>\nthe spin-1\/2 system. Rather than a mathematically rigorous derivation, the relationships are found<br \/>\nby forcing expectation values of the different basis states to have the properties we expect of a<br \/>\nclassical, geometric coordinate system. The process highlights the correspondence of quantum angular<br \/>\nmomentum with classical notions of geometric orthogonality, even for the inherently non-classical<br \/>\nspin-1\/2 system. In the process, differences in and connections between geometrical space and<br \/>\nHilbert space are illustrated.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Using concepts of geometric orthogonality and linear independence, we logically deduce the form of<br \/>\nthe Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of<br \/>\nthe spin-1\/2 system. Rather than a mathematically ri&#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-247469","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\/247469","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=247469"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/247469\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=247469"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=247469"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=247469"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}