{"id":222971,"date":"2025-10-06T20:07:55","date_gmt":"2025-10-07T01:07:55","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/10\/matter-wave"},"modified":"2025-10-06T20:07:55","modified_gmt":"2025-10-07T01:07:55","slug":"matter-wave","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/10\/matter-wave","title":{"rendered":"Matter wave"},"content":{"rendered":"<p style=\"padding-right: 20px\"><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/matter-wave.jpg\"><\/a><\/p>\n<p>Schr\u00f6dinger applied Hamilton\u2019s optico-mechanical analogy to develop his wave mechanics for subatomic particles.<sup id= cite_ref-67 class= reference> [ 67 ] <\/sup><sup class= reference nowrap> : xi <\/sup> Consequently, wave solutions to the Schr\u00f6dinger equation share many properties with results of light wave optics. In particular, Kirchhoff\u2019s diffraction formula works well for electron optics<sup id= cite_ref-BornAndWolf_29-1 class= reference> [ 29 ] <\/sup><sup class= reference nowrap> : 745 <\/sup> and for atomic optics.<sup id= cite_ref-adams_68-0 class= reference> [ 68 ] <\/sup> The approximation works well as long as the electric fields change more slowly than the <i>de Broglie wavelength<\/i>. Macroscopic apparatus fulfill this condition; slow electrons moving in solids do not.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Schr\u00f6dinger applied Hamilton\u2019s optico-mechanical analogy to develop his wave mechanics for subatomic particles. [ 67 ] : xi Consequently, wave solutions to the Schr\u00f6dinger equation share many properties with results of light wave optics. In particular, Kirchhoff\u2019s diffraction formula works well for electron optics [ 29 ] : 745 and for atomic optics. [ 68 [\u2026]<\/p>\n","protected":false},"author":709,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[41,48],"tags":[],"class_list":["post-222971","post","type-post","status-publish","format-standard","hentry","category-information-science","category-particle-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/222971","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/709"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=222971"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/222971\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=222971"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=222971"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=222971"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}