{"id":273592,"date":"2016-09-07T02:00:00","date_gmt":"2016-09-06T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=4376d9bf7daf39fa6424f91acb72396a"},"modified":"2016-09-07T02:00:00","modified_gmt":"2016-09-06T23:00:00","slug":"the-kronecker-product-and-some-of-its-physical-applications","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=273592","title":{"rendered":"The Kronecker product and some of its physical applications"},"content":{"rendered":"<p>In a typical introductory course on quantum mechanics the student has to face two quite different<br \/>\noperator products. One of them leads to, for example, commutators and the uncertainty principle, and<br \/>\nthe other appears when one goes from a one-particle system to a multi-particle one. The latter gives<br \/>\nrise to the direct or tensor product of operators and vector spaces, and to the Kronecker product of<br \/>\nthe matrix representations of the operators. We illustrate the practical utility of the Kronecker<br \/>\nproduct by means of two spin systems commonly discussed in introductory courses on quantum mechanics<br \/>\nand also by means of a simple model for the interpretation of the NMR signal produced by two<br \/>\ninteracting protons.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In a typical introductory course on quantum mechanics the student has to face two quite different<br \/>\noperator products. One of them leads to, for example, commutators and the uncertainty principle, and<br \/>\nthe other appears when one goes from a one-particle&#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-273592","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\/273592","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=273592"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/273592\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=273592"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=273592"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=273592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}