{"id":157636,"date":"2023-09-06T13:54:04","date_gmt":"2023-09-06T08:24:04","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=157636"},"modified":"2023-09-06T13:54:06","modified_gmt":"2023-09-06T08:24:06","slug":"in-a-certain-two-dimensional-lattice-the-energy-dispersion-of-the-electrons-is","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/in-a-certain-two-dimensional-lattice-the-energy-dispersion-of-the-electrons-is\/","title":{"rendered":"In a certain two-dimensional lattice, the energy dispersion of the electrons is"},"content":{"rendered":"\n<p>Q. In a certain two-dimensional lattice, the energy dispersion of the electrons is<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" width=\"409\" height=\"84\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-801.png\" alt=\"\" class=\"wp-image-157639\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-801.png 409w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-801-300x62.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><\/figure>\n\n\n\n<p>where \ud835\udc58\u20d7\u2192\u00a0= (\ud835\udc58<sub>\ud835\udc65<\/sub> , \ud835\udc58<sub>\ud835\udc66<\/sub>) denotes the wave vector, \ud835\udc4e is the lattice constant and \ud835\udc61 is a constant in units of eV. In this lattice the effective mass tensor \ud835\udc5a<sub>\ud835\udc56\ud835\udc57<\/sub> of electrons calculated at the center of the Brillouin zone has the form <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"153\" height=\"87\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-802.png\" alt=\"\" class=\"wp-image-157642\"\/><\/figure>\n\n\n\n<p>The value of \ud835\udefc (rounded off to three decimal places) is \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n\n\n\n<p>Ans: 0.33<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. In a certain two-dimensional lattice, the energy dispersion of the electrons is where \ud835\udc58\u20d7\u2192\u00a0= (\ud835\udc58\ud835\udc65 , \ud835\udc58\ud835\udc66) denotes the wave vector, \ud835\udc4e is the lattice constant and \ud835\udc61 is a constant in units of eV. In this lattice the effective mass tensor \ud835\udc5a\ud835\udc56\ud835\udc57 of electrons calculated at the center of the Brillouin zone has [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":157648,"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-157636","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\/157636","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=157636"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157636\/revisions"}],"predecessor-version":[{"id":157651,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157636\/revisions\/157651"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/157648"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=157636"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=157636"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=157636"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}