{"id":3983,"date":"2024-09-19T13:03:48","date_gmt":"2024-09-19T13:03:48","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=3983"},"modified":"2024-09-19T13:03:49","modified_gmt":"2024-09-19T13:03:49","slug":"the-essentials-of-quantum-mechanics","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/09\/19\/the-essentials-of-quantum-mechanics\/","title":{"rendered":"The Essentials of Quantum Mechanics"},"content":{"rendered":"\n<p>This is the same as the condition h\u03c8|\u03c8i = 1, i.e., the state |\u03c8i must be<\/p>\n\n\n\n<p>normalized, or be a unit vector in Hilbert space. A state vector that does not<\/p>\n\n\n\n<p>have unit norm can be normalized by dividing it by its norm.<\/p>\n\n\n\n<p>The \ufb01rst axiom of quantum mechanics is a statement that embodies all<\/p>\n\n\n\n<p>this.<\/p>\n\n\n\n<p>Exercise 3.1. Normalize the vectors<\/p>\n\n\n\n<p>&#8220;<\/p>\n\n\n\n<p>1<\/p>\n\n\n\n<p>1<\/p>\n\n\n\n<p>#<\/p>\n\n\n\n<p>and<\/p>\n\n\n\n<p>&#8220;<\/p>\n\n\n\n<p>1<\/p>\n\n\n\n<p>\u22121<\/p>\n\n\n\n<p>#<\/p>\n\n\n\n<p>. Show that they are<\/p>\n\n\n\n<p>orthogonal.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Exercise 3.2. Normalize the state |0i \u2212 2i|1i.<\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>This is the same as the condition h\u03c8|\u03c8i = 1, i.e., the state |\u03c8i must be normalized, or be a unit vector in Hilbert space. A state vector that does not have unit norm can be normalized by dividing it by its norm. The \ufb01rst axiom of quantum mechanics is a statement that embodies all [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3974,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[489],"tags":[],"class_list":["post-3983","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-4-quantum-mechanics"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/quantum-computer-1.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3983","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=3983"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3983\/revisions"}],"predecessor-version":[{"id":3984,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3983\/revisions\/3984"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/3974"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=3983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=3983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=3983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}