{"id":140,"date":"2018-12-23T22:49:53","date_gmt":"2018-12-23T21:49:53","guid":{"rendered":"http:\/\/www.leotheodon.com\/V4\/?p=140"},"modified":"2019-01-30T13:00:00","modified_gmt":"2019-01-30T12:00:00","slug":"projet-proprietes-quantiques-dune-particule","status":"publish","type":"post","link":"https:\/\/www.leotheodon.com\/V4\/2018\/12\/23\/projet-proprietes-quantiques-dune-particule\/","title":{"rendered":"[Projet] Propri\u00e9t\u00e9s quantiques d’une particule"},"content":{"rendered":"\n

Lors du premier semestre de L3-Pysique fondamentale, et apr\u00e8s avoir pu assister \u00e0 quelques cours de m\u00e9canique quantique, nous nous sommes vu proposer un projet m\u00ealant physique, math\u00e9matiques et informatique.<\/p>\n\n\n\n

Le but est d’\u00e9tudier les propri\u00e9t\u00e9s de diffusion d’une particule quantique soumise \u00e0 une \u00e9nergie potentielle rectangulaire en r\u00e9solvant l’\u00e9quation de Schr\u00f6dinger et ce, de deux mani\u00e8re diff\u00e9rentes. En effectuant un calcul analytique direct d’une part, et avec un calcul matriciel faisant appel aux fonctions de Green <\/em>d’autre part.<\/p>\n\n\n\n

Nous calculerons \u00e9galement les coefficients de r\u00e9flexion et de transissions pour diff\u00e9rentes \u00e9nergies et masses de la particule (\u00e9lectron ou proton) et diff\u00e9rentes valeurs de potentiel afin de calculer la probabilit\u00e9 de passage par effet tunnel. <\/p>\n\n\n\n

Typiquement, notre Hamiltonien s’\u00e9crira de la fa\u00e7on suivante:<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ H = -\dfrac{\hbar^2}{2m}\dfrac{d^2}{dx^2}+V(x)\]\"<\/p><\/p>\n\n\n\n

L’espace sera s\u00e9par\u00e9 en trois parties, selon que le potentiel \"V\" est nul ou non. Le probl\u00e8me se r\u00e9duit ainsi \u00e0 une simple r\u00e9solution de l’\u00e9quation de Schr\u00f6dinger ind\u00e9pendante du temps dans un espace \u00e0 une dimension. Un probl\u00e8me extr\u00eamement classique.<\/p>\n\n\n\n

Ce projet a bien entendu abouti \u00e0 la r\u00e9daction d’un rapport, disponible ci-dessous au format pdf, et les sources du programme MATLAB <\/em>sont \u00e9galement t\u00e9l\u00e9chargeables.<\/p>\n\n\n\n

T\u00e9l\u00e9charger :<\/strong><\/p>\n\n\n\n

– Le rapport au format pdf :<\/a>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n
– Source(Pro_113) :<\/a>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n
– Source(Pro_1132) :<\/a>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n
– Source(Pro_1133) :<\/a>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n
– Source(Pro_231) :<\/a>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Lors du premier semestre de L3-Pysique fondamentale, et apr\u00e8s avoir pu assister \u00e0 quelques cours de m\u00e9canique quantique…<\/p>\n","protected":false},"author":1,"featured_media":185,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rop_custom_images_group":[],"rop_custom_messages_group":[],"rop_publish_now":"initial","rop_publish_now_accounts":[],"rop_publish_now_history":[],"rop_publish_now_status":"pending","_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[3,32,5,4],"tags":[33,26,37,27,34,11],"class_list":["post-140","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-education","category-informatique","category-math","category-physique","tag-informatique","tag-maths","tag-matlab","tag-physique","tag-projet","tag-rapport"],"_links":{"self":[{"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/posts\/140","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/comments?post=140"}],"version-history":[{"count":13,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/posts\/140\/revisions"}],"predecessor-version":[{"id":283,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/posts\/140\/revisions\/283"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/media\/185"}],"wp:attachment":[{"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/media?parent=140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/categories?post=140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.leotheodon.com\/V4\/wp-json\/wp\/v2\/tags?post=140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}