{"id":457,"date":"2021-04-13T11:30:59","date_gmt":"2021-04-13T10:30:59","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/MathsUGProjects\/?p=457"},"modified":"2022-11-11T10:24:55","modified_gmt":"2022-11-11T10:24:55","slug":"embedded-eigenvalues-of-schrodinger-operators-prof-k-m-schmidt","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/embedded-eigenvalues-of-schrodinger-operators-prof-k-m-schmidt\/","title":{"rendered":"Embedded Eigenvalues of Schr\u00f6dinger Operators &#8211; Supervisor: Prof Karl Schmidt"},"content":{"rendered":"<p style=\"color: #383735\"><strong>Title of project:<\/strong><br \/>\nEmbedded Eigenvalues of Schr\u00f6dinger Operators<\/p>\n<p style=\"color: #383735\"><strong>Code:<\/strong><br \/>\nKMS2122B<\/p>\n<p style=\"color: #383735\"><strong>Supervisor:\u00a0<\/strong><br \/>\nProf Karl Schmidt<\/p>\n<p><strong>Project description:<\/strong><br \/>\nThe spectrum of Schr\u00f6dinger operators, corresponding to the set of admissible energies of a quantum mechanical system, consists of a half-line of continuous spectrum and additional discrete eigenvalues in many physically relevant situations. It is a rarer and more unstable phenomenon to have eigenvalues embedded inside the continuous spectrum. A first example of such a Schr\u00f6dinger operator was first constructed by John von Neumann and Eugene Wigner in 1929.<\/p>\n<p>The project will be focussed on understanding a recently published construction which allows to ensure the presence of any finite number of predefined embedded eigenvalues. This challenging project gives the opportunity to learn and apply some techniques of the spectral analysis of ordinary differential operators.<\/p>\n<p style=\"color: #383735\"><strong>Prerequisite 2nd\/3rd year modules:<\/strong><br \/>\nMA2006 Real Analysis<br \/>\nMA3012 Ordinary Differential Equations<br \/>\nMA3005 Introduction to Functional and Fourier Analysis<\/p>\n<p style=\"color: #383735\"><strong>Number of students who could be supervised for this project:<\/strong><br \/>\n1<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title of project: Embedded Eigenvalues of Schr\u00f6dinger Operators Code: KMS2122B Supervisor:\u00a0 Prof Karl Schmidt Project description: The spectrum of Schr\u00f6dinger operators, corresponding to the set of admissible energies of a quantum mechanical system, consists of a half-line of continuous spectrum and additional discrete eigenvalues in many physically relevant situations. It is a rarer and more &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/embedded-eigenvalues-of-schrodinger-operators-prof-k-m-schmidt\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Embedded Eigenvalues of Schr\u00f6dinger Operators &#8211; Supervisor: Prof Karl Schmidt<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[2,4,8],"tags":[],"class_list":["post-457","post","type-post","status-publish","format-standard","hentry","category-2021-2022","category-double","category-yr-4-description-2021-2022"],"aioseo_notices":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/457","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/comments?post=457"}],"version-history":[{"count":4,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/457\/revisions"}],"predecessor-version":[{"id":2035,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/457\/revisions\/2035"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/media?parent=457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/categories?post=457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/tags?post=457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}