{"id":157371,"date":"2023-09-05T15:41:17","date_gmt":"2023-09-05T10:11:17","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=157371"},"modified":"2023-09-05T15:41:22","modified_gmt":"2023-09-05T10:11:22","slug":"the-hamiltonian-for-a-quantum-harmonic-oscillator-of-mass-%f0%9d%91%9a-in-three-dimensions-is","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/the-hamiltonian-for-a-quantum-harmonic-oscillator-of-mass-%f0%9d%91%9a-in-three-dimensions-is\/","title":{"rendered":"The Hamiltonian for a quantum harmonic oscillator of mass \ud835\udc5a in three dimensions is"},"content":{"rendered":"\n<p>Q. The Hamiltonian for a quantum harmonic oscillator of mass \ud835\udc5a in three dimensions is<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"148\" height=\"49\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-763.png\" alt=\"\" class=\"wp-image-157375\"\/><\/figure>\n\n\n\n<p>where \ud835\udf14 is the angular frequency. The expectation value of \ud835\udc5f<sup>2<\/sup> in the first excited state of the oscillator in units of <\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-764.png\" alt=\"\" class=\"wp-image-157379\" style=\"width:52px;height:62px\" width=\"52\" height=\"62\"\/><\/figure>\n\n\n\n<p>(rounded off to one decimal place) is<\/p>\n\n\n\n<p>Ans: 2.5<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"449\" height=\"52\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-765.png\" alt=\"\" class=\"wp-image-157381\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-765.png 449w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-765-300x35.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"507\" height=\"150\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-766.png\" alt=\"\" class=\"wp-image-157386\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-766.png 507w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-766-300x89.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. The Hamiltonian for a quantum harmonic oscillator of mass \ud835\udc5a in three dimensions is where \ud835\udf14 is the angular frequency. The expectation value of \ud835\udc5f2 in the first excited state of the oscillator in units of (rounded off to one decimal place) is Ans: 2.5 Sol:<\/p>\n","protected":false},"author":419,"featured_media":157388,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-157371","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157371","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=157371"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157371\/revisions"}],"predecessor-version":[{"id":157389,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157371\/revisions\/157389"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/157388"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=157371"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=157371"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=157371"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}