{"id":320488,"date":"2021-03-29T21:00:45","date_gmt":"2021-03-29T21:00:45","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=320488"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=320488","title":{"rendered":"\u0410\u043d\u0438\u043c\u0430\u0446\u0438\u044f \u0432\u043e\u043b\u043d\u043e\u0432\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430 (\u03c8) \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e Python (\u0441 \u043f\u043e\u043b\u043d\u044b\u043c \u043a\u043e\u0434\u043e\u043c)"},"content":{"rendered":"\n<div class=\"post__text post__text_v2\" id=\"post-content-body\">\n<figure class=\"full-width\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/184\/3b5\/b3d\/1843b5b3d61225499d7943cadffeff86.png\" width=\"729\" height=\"438\"><figcaption><\/figcaption><\/figure>\n<p>\u0414\u0432\u043e\u0439\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043f\u0440\u0438\u0440\u043e\u0434\u0430 \u043c\u0430\u0442\u0435\u0440\u0438\u0438 \u2014 \u0448\u0438\u0440\u043e\u043a\u043e \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u0441\u0440\u0435\u0434\u0438 \u0444\u0438\u0437\u0438\u043a\u043e\u0432. \u0412\u0435\u0449\u0435\u0441\u0442\u0432\u043e \u043d\u0430 \u0430\u0442\u043e\u043c\u043d\u043e\u043c \u0443\u0440\u043e\u0432\u043d\u0435 \u0432 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u044f\u0445 \u0432\u0435\u0434\u0451\u0442 \u0441\u0435\u0431\u044f \u043a\u0430\u043a \u0447\u0430\u0441\u0442\u0438\u0446\u044b, \u0430 \u0432 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u2014 \u043a\u0430\u043a \u0432\u043e\u043b\u043d\u044b. \u0427\u0442\u043e\u0431\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c \u044d\u0442\u043e, \u043c\u044b \u0432\u0432\u043e\u0434\u0438\u043c \u0432\u043e\u043b\u043d\u043e\u0432\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u03c8(x, t), \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u043d\u0435 \u0444\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0447\u0430\u0441\u0442\u0438\u0446\u044b, \u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0432 \u0434\u0430\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. \u0412\u043e\u043b\u043d\u043e\u0432\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u03c8(x, t), \u0438\u043b\u0438 \u043f\u043e\u043b\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0435\u0442, \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u0441\u0430\u043c\u043e\u043c\u0443 \u0432\u0430\u0436\u043d\u043e\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0432 \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445, \u043f\u043e \u043a\u0440\u0430\u0439\u043d\u0435\u0439 \u043c\u0435\u0440\u0435 \u0434\u043b\u044f \u0444\u0438\u0437\u0438\u043a\u043e\u0432, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430.<\/p>\n<h4>\u041e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430<\/h4>\n<p>\u041c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430 \u0432 \u043e\u0434\u043d\u043e\u043c \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u0438. \u041c\u0435\u0442\u043e\u0434 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0432\u043e\u043b\u043d\u043e\u0432\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0434\u0432\u0443\u0445 \u0438\u043b\u0438 \u0442\u0440\u0451\u0445 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u044f\u0445 \u0432 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u043c \u0442\u0430\u043a\u043e\u0439 \u0436\u0435, \u043a\u0430\u043a \u0438 \u0434\u043b\u044f \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e. \u041d\u043e \u0434\u043b\u044f \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0438 \u0440\u0430\u0434\u0438 \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u043f\u0440\u0438\u0434\u0435\u0440\u0436\u0438\u0432\u0430\u0442\u044c\u0441\u044f \u043e\u0434\u043d\u043e\u0433\u043e \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u044f. \u0412\u044b\u0432\u0435\u0434\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430 \u0434\u043b\u044f \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u0441\u043b\u0443\u0447\u0430\u044f.<\/p>\n<figure class=\"full-width\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3db\/a8f\/cb3\/3dba8fcb37dd5c328d058b2da154f793.png\" width=\"794\" height=\"439\"><figcaption><\/figcaption><\/figure>\n<h4>\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0432 \u044f\u0449\u0438\u043a\u0435 \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u041a\u0440\u0430\u043d\u043a\u0430 \u2014 \u041d\u0438\u043a\u043e\u043b\u0441\u043e\u043d\u0430<\/h4>\n<figure class=\"full-width\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c17\/461\/ea0\/c17461ea0d7d915a8c497c0f9413572e.png\" width=\"797\" height=\"449\"><figcaption><\/figcaption><\/figure>\n<p>\u0420\u0435\u0448\u0438\u043c \u0432\u043e\u043b\u043d\u043e\u0432\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043d\u0430\u0448\u0435\u0439 \u0447\u0430\u0441\u0442\u0438\u0446\u044b, \u043d\u0430\u0445\u043e\u0434\u044f\u0449\u0435\u0439\u0441\u044f \u0432 \u044f\u0449\u0438\u043a\u0435 \u0441 \u043d\u0435\u043f\u0440\u043e\u043d\u0438\u0446\u0430\u0435\u043c\u044b\u043c\u0438 \u0441\u0442\u0435\u043d\u043a\u0430\u043c\u0438. \u0418\u0434\u0435\u044f \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u0440\u0435\u0448\u0438\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0440\u0430\u0437\u043c\u0435\u0440\u0430. \u041d\u043e \u043f\u043e\u0447\u0435\u043c\u0443 \u0432 \u043d\u0435\u043f\u0440\u043e\u043d\u0438\u0446\u0430\u0435\u043c\u044b\u0445 \u0441\u0442\u0435\u043d\u0430\u0445? \u042d\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0437\u0430\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0432\u043e\u043b\u043d\u043e\u0432\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0440\u0430\u0432\u043d\u044f\u0442\u044c\u0441\u044f \u043d\u0443\u043b\u044e \u043d\u0430 \u0441\u0442\u0435\u043d\u043a\u0430\u0445, \u0447\u0442\u043e \u043c\u044b \u043f\u043e\u043b\u043e\u0436\u0438\u043c \u043f\u0440\u0438 x=0 \u0438 x=L. \u041c\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0439 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c\u044e \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u043c\u0435\u0442\u043e\u0434 \u042d\u0439\u043b\u0435\u0440\u0430.<\/p>\n<figure class=\"full-width\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/beb\/77d\/4bd\/beb77d4bdbd4ac64d9f7bbe3b4d9fdab.png\" width=\"1231\" height=\"449\"><figcaption><\/figcaption><\/figure>\n<p>\u041f\u0440\u0438\u0432\u0435\u0434\u0451\u043d\u043d\u044b\u0439 \u0432\u044b\u0448\u0435 \u0432\u044b\u0432\u043e\u0434 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043d\u0430\u043c \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0432\u043d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430. \u0413\u0440\u0430\u043d\u0438\u0447\u043d\u044b\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u043f\u0440\u0438 x=0 \u0438 x=L \u0434\u043b\u044f \u0432\u0441\u0435\u0445 t \u0432\u043e\u043b\u043d\u043e\u0432\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u03c8(x, t)=0. \u041c\u0435\u0436\u0434\u0443 \u044d\u0442\u0438\u043c\u0438 \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0442\u043e\u0447\u043a\u0438 \u0441\u0435\u0442\u043a\u0438 \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 a, 2a, 3a \u0438 \u0442\u0430\u043a \u0434\u0430\u043b\u0435\u0435. \u0421\u0433\u0440\u0443\u043f\u043f\u0438\u0440\u0443\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u03c8(x, t) \u0432 \u044d\u0442\u0438\u0445 \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 \u0432 \u0432\u0435\u043a\u0442\u043e\u0440.<\/p>\n<figure class=\"full-width\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/685\/2ae\/6fb\/6852ae6fb7680a6219c5fbdaaaf0ea28.png\" width=\"1204\" height=\"667\"><figcaption><\/figcaption><\/figure>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0432\u0441\u0451 \u043f\u0440\u043e\u0441\u0442\u043e, \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f: A\u03c8(t + h) = B\u03c8(t), \u0433\u0434\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b A \u0438 B \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u043c\u0438 \u0438 \u0442\u0440\u0451\u0445\u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438. \u041d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0431\u0443\u0434\u0435\u0442 \u0438\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0432\u043e\u043b\u043d\u043e\u0432\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043d\u0430 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u043c \u0448\u0430\u0433\u0435 t = 0, \u03c8(0). \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u03c8(h), \u0430 \u0437\u0430\u0442\u0435\u043c, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u03c8(h), \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u03c8(2h) \u0438 \u0442\u0430\u043a \u0434\u0430\u043b\u0435\u0435. \u0412 \u043c\u043e\u043c\u0435\u043d\u0442 t = 0 \u0432\u043e\u043b\u043d\u043e\u0432\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u03c8(0) \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<figure class=\"full-width\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/485\/a1a\/9b2\/485a1a9b24a77c7a0734edc69e259670.png\" width=\"567\" height=\"131\"><figcaption><\/figcaption><\/figure>\n<p>\u042d\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u03c8(0) \u043d\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u043d\u043e, \u0438 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u043e\u0431\u0449\u0438\u0439 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f, \u0447\u0442\u043e\u0431\u044b \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u0447\u0442\u043e \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0434\u043b\u044f \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0432 \u0435\u0434\u0438\u043d\u0438\u0446\u0443.<\/p>\n<h4>\u0410\u043d\u0438\u043c\u0430\u0446\u0438\u044f \u0432\u043e\u043b\u043d\u043e\u0432\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0432 \u043a\u043e\u0440\u043e\u0431\u043a\u0435<\/h4>\n<p>\u041c\u044b \u043f\u043e\u043f\u0440\u043e\u0431\u0443\u0435\u043c \u043e\u0436\u0438\u0432\u0438\u0442\u044c \u0447\u0430\u0441\u0442\u0438\u0446\u0443 \u0432 \u043a\u043e\u0440\u043e\u0431\u043a\u0435 \u0441 \u043d\u0435\u043f\u0440\u043e\u043d\u0438\u0446\u0430\u0435\u043c\u044b\u043c\u0438 \u0441\u0442\u0435\u043d\u043a\u0430\u043c\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043c\u0435\u0442\u043e\u0434 \u041a\u0440\u0430\u043d\u043a\u0430 \u2014 \u041d\u0438\u043a\u043e\u043b\u0441\u043e\u043d\u0430. \u041d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0431\u0443\u0434\u0435\u0442 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440 \u03c8(x, t) \u043d\u0430 \u0432\u0441\u0435\u0445 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0448\u0430\u0433\u0430\u0445 \u043f\u043e \u0441\u0435\u0442\u043a\u0435, \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u0443\u044e \u0432\u043e\u043b\u043d\u043e\u0432\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u03c8(0) \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0441\u0440\u0435\u0437\u044b (N = 1000) \u0441 \u0434\u043b\u0438\u043d\u043e\u0439 \u0441\u0440\u0435\u0437\u0430 = L\/N.<\/p>\n<figure class=\"full-width\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c30\/58f\/911\/c3058f91155a1f5e588e04f0b02ca421.png\" width=\"762\" height=\"558\"><figcaption><\/figcaption><\/figure>\n<details class=\"spoiler\">\n<summary>\u0414\u043b\u0438\u043d\u043d\u0430\u044f \u043f\u0440\u043e\u0441\u0442\u044b\u043d\u044f \u0441 \u043a\u043e\u0434\u043e\u043c<\/summary>\n<div class=\"spoiler__content\">\n<pre><code class=\"python\">import numpy  as np from pylab import * from matplotlib import pyplot as plt from matplotlib import animation #matplotlib.use('GTK3Agg')   # from matplotlib import interactive # interactive(True)  ########################################Variables###################################################################################################### N_Slices = 1000            #Number of slices in the box  Time_step = 1e-18          #Time step for each iteration  Mass = 9.109e-31           #mass of electron  plank = 1.0546e-36         #Planks constant  L_Box = 1e-9           #Length of the box Grid = L_Box\/N_Slices                             #Lenght of each slice   #####################################Si(0) using the given equation ###############################################################################   Si_0 = np.zeros(N_Slices+1,complex)                        #Initiating Si funtion at time step = 0  x = np.linspace(0,L_Box,N_Slices+1)                             def G_Equation(x):     x_0 = L_Box\/2     Sig = 1e-10     k = 5e10     result  = exp(-(x-x_0)**2\/2\/Sig**2)*exp(1j*k*x)       #Given Equation at t = 0     return result Si_0[:] = G_Equation(x)                                     #Si funtion at time step = 0              #######################################V = Bxsi(0)################################################################################ a_1 = 1 + Time_step*plank*1j\/(2*Mass*(Grid**2))   #Diagonal of A Tridiagonal matrix a_2 = -Time_step*plank*1j\/(4*Mass*Grid**2)        #Up and Down to A Tridiagonal matrix b_1 =  1 - Time_step*plank*1j\/(2*Mass*(Grid**2))  #Diagonal of B Tridiagonal matrix b_2 =  Time_step*plank*1j\/(4*Mass*Grid**2)        #Up and Down to B Tridiagonal matrix    BxSi_0 = []                                                      #V = BxSi and si funtion at x = 0 for i in range(1000):     if i == 0:         BxSi_0.append(b_1*Si_0[0] + b_2*(Si_0[1]))                   #V can be maipulated by the equation in Text book               else:                                                              BxSi_0.append(b_1*Si_0[i] + b_2*(Si_0[i+1] + Si_0[i-1])) BxSi_0 = np.array(BxSi_0)  #####################################Tri Diagonal matrix algorithm#####################################################################################  def TDMAsolver(a, b, c, d):                                   #Instead of solving using Numpy.linalg, it is prefered to Use      nf = len(d)                                               #Tri Diagonal Matrix algorithm      ac, bc, cc, dc = map(np.array, (a, b, c, d))              # a,b,c's are up,dia,down element in tridiagonl matrix A     for it in range(1, nf):                                  #AX = d         mc = ac[it-1]\/bc[it-1]         bc[it] = bc[it] - mc*cc[it-1]          dc[it] = dc[it] - mc*dc[it-1]         \t         xc = bc     xc[-1] = dc[-1]\/bc[-1]      for il in range(nf-2, -1, -1):         xc[il] = (dc[il]-cc[il]*xc[il+1])\/bc[il]     return xc   global a                    #A matrix is fixed through out the problem, so it is good to globalize the variables  global b global c b = N_Slices*[a_1]          #In A matrix, Both  Up,Down elements are a_2 and diag matrix is a_1 a = (N_Slices-1)*[a_2] c = (N_Slices-1)*[a_2] ####################################Si 1st funtion solver####################################################################################  global Si_1                                 #First si_funtion usinf Axsi(0+h) = BxSi(0) Si_1 = TDMAsolver(a, b, c, BxSi_0)          #This can be solved by TDM(A,BxSi(0))   ###################################A funtion which caliculates si at each step##################################################################################### global Si_sd                            #AxSi_stepup = BxSi_stepdown Si_sd = {}                              #At first Buckting Si_stepdown in to directry which we can using for finding Si_stepup  def sifuntion(i):                       #In next iteration, Last iteration Si_stepup will be this iteration's Si_stepdown     if i == 0:         Si_sd[0] = Si_1         return Si_1     else:         Si_stepdown = Si_sd[i-1]         V = np.zeros(N_Slices,complex)         V[0] = b_1*Si_stepdown[0] + b_2*(Si_stepdown[1])         V[1:N_Slices-1] = b_1*Si_stepdown[1:N_Slices-1] + b_2*(Si_stepdown[2:N_Slices] + Si_stepdown[0:N_Slices-2])         V[N_Slices-1] = b_1*Si_stepdown[N_Slices-1]+ b_2*(Si_stepdown[N_Slices-2])         Si_stepup = TDMAsolver(a, b, c, V)         Si_sd[i] = Si_stepup          x = Si_stepup.real         return x ####################################Animating#######################################################################################       fig = plt.figure() ax = plt.axes(xlim=(0, 1000), ylim=(-1.5, 1.5)) line, = ax.plot([], [], lw=5) ax.legend(prop=dict(size=20)) ax.set_facecolor('black') ax.patch.set_alpha(0.8) ax.set_xlabel('$x$',fontsize = 15,color = 'blue') ax.set_ylabel(r'$|\\psi(x)|$',fontsize = 15,color = 'blue') ax.grid(color = 'blue') ax.set_title(r'$|\\psi(x)|$ vs $x$', color='blue',fontsize = 15 ) line, = ax.step([], [])  def init():     line.set_data([], [])     return line,   def animate(i):     x = np.linspace(0, 1000, num=1000)     y = sifuntion(i)     line.set_data(x, y)     line.set_color('red')     return line,  anim = animation.FuncAnimation(fig, animate, init_func=init,                                frames=10**5, interval=1, blit=True)#5*10**5  plt.vlines(1, -5, 5, linestyles = 'solid', color= 'green',lw=5) plt.vlines(999, -5, 5, linestyles = 'solid', color= 'green',lw=5) plt.text(1,1,'Boundary',rotation=90,color= 'green' ) plt.text(975,1,'Boundary',rotation=90,color= 'green' ) plt.figure(figsize=(10,10)) plt.show()     # Writer = animation.writers['ffmpeg'] # writer = Writer() # anim.save('im.mp4', writer=writer) <\/code><\/pre>\n<\/div>\n<\/details>\n<figure class=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/5dc\/d67\/e0b\/5dcd67e0bd804aed5ea7f488a557f4aa.jpg\" width=\"894\" height=\"120\"><figcaption><\/figcaption><\/figure>\n<p><a href=\"https:\/\/skillfactory.ru\/courses\/?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_ALLCOURSES&amp;utm_term=regular&amp;utm_content=290321\">\u0423\u0437\u043d\u0430\u0439\u0442\u0435<\/a>, \u043a\u0430\u043a \u043f\u0440\u043e\u043a\u0430\u0447\u0430\u0442\u044c\u0441\u044f \u0432 \u0434\u0440\u0443\u0433\u0438\u0445 \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u044f\u0445 \u0438\u043b\u0438 \u043e\u0441\u0432\u043e\u0438\u0442\u044c \u0438\u0445 \u0441 \u043d\u0443\u043b\u044f:<\/p>\n<ul>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/dstpro?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_DSPR&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Data Scientist<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/dataanalystpro?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_DAPR&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Data Analyst<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/dataengineer?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_DEA&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 \u043f\u043e Data Engineering<\/a><\/p>\n<\/li>\n<\/ul>\n<details class=\"spoiler\">\n<summary>\u0414\u0440\u0443\u0433\u0438\u0435 \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u0438 \u0438 \u043a\u0443\u0440\u0441\u044b<\/summary>\n<div class=\"spoiler__content\">\n<p><strong>\u041f\u0420\u041e\u0424\u0415\u0421\u0421\u0418\u0418<\/strong><\/p>\n<ul>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/python-fullstack-web-developer?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_FPW&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Fullstack-\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a \u043d\u0430 Python<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/java?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_JAVA&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Java-\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/java-qa-engineer?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_QAJA&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f QA-\u0438\u043d\u0436\u0435\u043d\u0435\u0440 \u043d\u0430 JAVA<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/frontend?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_FR&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Frontend-\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/cybersecurity?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_HACKER&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f \u042d\u0442\u0438\u0447\u043d\u044b\u0439 \u0445\u0430\u043a\u0435\u0440<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/cplus?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_CPLUS&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f C++ \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/game-dev?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_GAMEDEV&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a \u0438\u0433\u0440 \u043d\u0430 Unity<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/webdev?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_WEBDEV&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f \u0412\u0435\u0431-\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/iosdev?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_IOSDEV&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f iOS-\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a \u0441 \u043d\u0443\u043b\u044f<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/android?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_ANDR&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Android-\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a \u0441 \u043d\u0443\u043b\u044f<\/a><\/p>\n<\/li>\n<\/ul>\n<p><strong>\u041a\u0423\u0420\u0421\u042b<\/strong><\/p>\n<ul>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/ml-programma-machine-learning-online?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_ML&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 \u043f\u043e Machine Learning<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/ml-and-dl?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_MLDL&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 &#171;Machine Learning \u0438 Deep Learning&#187;<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/math-stat-for-ds#syllabus?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_MAT&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 &#171;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0434\u043b\u044f Data Science&#187;<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/math_and_ml?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_MATML&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 &#171;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 Machine Learning \u0434\u043b\u044f Data Science&#187;&nbsp;<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/python-for-web-developers?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_PWS&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 &#171;Python \u0434\u043b\u044f \u0432\u0435\u0431-\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0438&#187;<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/algo?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_algo&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 &#171;\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u044b \u0438 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u044b \u0434\u0430\u043d\u043d\u044b\u0445&#187;<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/analytics?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_SDA&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 \u043f\u043e \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u043a\u0435 \u0434\u0430\u043d\u043d\u044b\u0445<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/devops?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_DEVOPS&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 \u043f\u043e DevOps<\/a><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/details>\n<\/div>\n<p> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habr.com\/ru\/company\/skillfactory\/blog\/549470\/\"> https:\/\/habr.com\/ru\/company\/skillfactory\/blog\/549470\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"\n<div class=\"post__text post__text_v2\" id=\"post-content-body\">\n<figure class=\"full-width\"><figcaption><\/figcaption><\/figure>\n<p>\u0414\u0432\u043e\u0439\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043f\u0440\u0438\u0440\u043e\u0434\u0430 \u043c\u0430\u0442\u0435\u0440\u0438\u0438 \u2014 \u0448\u0438\u0440\u043e\u043a\u043e \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u0441\u0440\u0435\u0434\u0438 \u0444\u0438\u0437\u0438\u043a\u043e\u0432. \u0412\u0435\u0449\u0435\u0441\u0442\u0432\u043e \u043d\u0430 \u0430\u0442\u043e\u043c\u043d\u043e\u043c \u0443\u0440\u043e\u0432\u043d\u0435 \u0432 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u044f\u0445 \u0432\u0435\u0434\u0451\u0442 \u0441\u0435\u0431\u044f \u043a\u0430\u043a \u0447\u0430\u0441\u0442\u0438\u0446\u044b, \u0430 \u0432 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u2014 \u043a\u0430\u043a \u0432\u043e\u043b\u043d\u044b. \u0427\u0442\u043e\u0431\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c \u044d\u0442\u043e, \u043c\u044b \u0432\u0432\u043e\u0434\u0438\u043c \u0432\u043e\u043b\u043d\u043e\u0432\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u03c8(x, t), \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u043d\u0435 \u0444\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0447\u0430\u0441\u0442\u0438\u0446\u044b, \u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0432 \u0434\u0430\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. \u0412\u043e\u043b\u043d\u043e\u0432\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u03c8(x, t), \u0438\u043b\u0438 \u043f\u043e\u043b\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0435\u0442, \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u0441\u0430\u043c\u043e\u043c\u0443 \u0432\u0430\u0436\u043d\u043e\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0432 \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445, \u043f\u043e \u043a\u0440\u0430\u0439\u043d\u0435\u0439 \u043c\u0435\u0440\u0435 \u0434\u043b\u044f \u0444\u0438\u0437\u0438\u043a\u043e\u0432, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430.<\/p>\n<h4>\u041e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430<\/h4>\n<p>\u041c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430 \u0432 \u043e\u0434\u043d\u043e\u043c \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u0438. \u041c\u0435\u0442\u043e\u0434 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0432\u043e\u043b\u043d\u043e\u0432\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0434\u0432\u0443\u0445 \u0438\u043b\u0438 \u0442\u0440\u0451\u0445 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u044f\u0445 \u0432 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u043c \u0442\u0430\u043a\u043e\u0439 \u0436\u0435, \u043a\u0430\u043a \u0438 \u0434\u043b\u044f \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e. \u041d\u043e \u0434\u043b\u044f \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0438 \u0440\u0430\u0434\u0438 \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u043f\u0440\u0438\u0434\u0435\u0440\u0436\u0438\u0432\u0430\u0442\u044c\u0441\u044f \u043e\u0434\u043d\u043e\u0433\u043e \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u044f. \u0412\u044b\u0432\u0435\u0434\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430 \u0434\u043b\u044f \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u0441\u043b\u0443\u0447\u0430\u044f.<\/p>\n<figure class=\"full-width\"><figcaption><\/figcaption><\/figure>\n<h4>\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0432 \u044f\u0449\u0438\u043a\u0435 \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u041a\u0440\u0430\u043d\u043a\u0430 \u2014 \u041d\u0438\u043a\u043e\u043b\u0441\u043e\u043d\u0430<\/h4>\n<figure class=\"full-width\"><figcaption><\/figcaption><\/figure>\n<p>\u0420\u0435\u0448\u0438\u043c \u0432\u043e\u043b\u043d\u043e\u0432\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043d\u0430\u0448\u0435\u0439 \u0447\u0430\u0441\u0442\u0438\u0446\u044b, \u043d\u0430\u0445\u043e\u0434\u044f\u0449\u0435\u0439\u0441\u044f \u0432 \u044f\u0449\u0438\u043a\u0435 \u0441 \u043d\u0435\u043f\u0440\u043e\u043d\u0438\u0446\u0430\u0435\u043c\u044b\u043c\u0438 \u0441\u0442\u0435\u043d\u043a\u0430\u043c\u0438. \u0418\u0434\u0435\u044f \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u0440\u0435\u0448\u0438\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0440\u0430\u0437\u043c\u0435\u0440\u0430. \u041d\u043e \u043f\u043e\u0447\u0435\u043c\u0443 \u0432 \u043d\u0435\u043f\u0440\u043e\u043d\u0438\u0446\u0430\u0435\u043c\u044b\u0445 \u0441\u0442\u0435\u043d\u0430\u0445? \u042d\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0437\u0430\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0432\u043e\u043b\u043d\u043e\u0432\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0440\u0430\u0432\u043d\u044f\u0442\u044c\u0441\u044f \u043d\u0443\u043b\u044e \u043d\u0430 \u0441\u0442\u0435\u043d\u043a\u0430\u0445, \u0447\u0442\u043e \u043c\u044b \u043f\u043e\u043b\u043e\u0436\u0438\u043c \u043f\u0440\u0438 x=0 \u0438 x=L. \u041c\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0439 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u044c\u044e \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u043c\u0435\u0442\u043e\u0434 \u042d\u0439\u043b\u0435\u0440\u0430.<\/p>\n<figure class=\"full-width\"><figcaption><\/figcaption><\/figure>\n<p>\u041f\u0440\u0438\u0432\u0435\u0434\u0451\u043d\u043d\u044b\u0439 \u0432\u044b\u0448\u0435 \u0432\u044b\u0432\u043e\u0434 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043d\u0430\u043c \u0440\u0435\u043a\u0443\u0440\u0441\u0438\u0432\u043d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0428\u0440\u0451\u0434\u0438\u043d\u0433\u0435\u0440\u0430. \u0413\u0440\u0430\u043d\u0438\u0447\u043d\u044b\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u043f\u0440\u0438 x=0 \u0438 x=L \u0434\u043b\u044f \u0432\u0441\u0435\u0445 t \u0432\u043e\u043b\u043d\u043e\u0432\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u03c8(x, t)=0. \u041c\u0435\u0436\u0434\u0443 \u044d\u0442\u0438\u043c\u0438 \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0442\u043e\u0447\u043a\u0438 \u0441\u0435\u0442\u043a\u0438 \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 a, 2a, 3a \u0438 \u0442\u0430\u043a \u0434\u0430\u043b\u0435\u0435. \u0421\u0433\u0440\u0443\u043f\u043f\u0438\u0440\u0443\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u03c8(x, t) \u0432 \u044d\u0442\u0438\u0445 \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0438\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 \u0432 \u0432\u0435\u043a\u0442\u043e\u0440.<\/p>\n<figure class=\"full-width\"><figcaption><\/figcaption><\/figure>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0432\u0441\u0451 \u043f\u0440\u043e\u0441\u0442\u043e, \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f: A\u03c8(t + h) = B\u03c8(t), \u0433\u0434\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b A \u0438 B \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u043c\u0438 \u0438 \u0442\u0440\u0451\u0445\u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438. \u041d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0431\u0443\u0434\u0435\u0442 \u0438\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0432\u043e\u043b\u043d\u043e\u0432\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043d\u0430 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u043c \u0448\u0430\u0433\u0435 t = 0, \u03c8(0). \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u03c8(h), \u0430 \u0437\u0430\u0442\u0435\u043c, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u03c8(h), \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u03c8(2h) \u0438 \u0442\u0430\u043a \u0434\u0430\u043b\u0435\u0435. \u0412 \u043c\u043e\u043c\u0435\u043d\u0442 t = 0 \u0432\u043e\u043b\u043d\u043e\u0432\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u03c8(0) \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<figure class=\"full-width\"><figcaption><\/figcaption><\/figure>\n<p>\u042d\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u03c8(0) \u043d\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u043d\u043e, \u0438 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u043e\u0431\u0449\u0438\u0439 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f, \u0447\u0442\u043e\u0431\u044b \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u0447\u0442\u043e \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0434\u043b\u044f \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0432 \u0435\u0434\u0438\u043d\u0438\u0446\u0443.<\/p>\n<h4>\u0410\u043d\u0438\u043c\u0430\u0446\u0438\u044f \u0432\u043e\u043b\u043d\u043e\u0432\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u0432 \u043a\u043e\u0440\u043e\u0431\u043a\u0435<\/h4>\n<p>\u041c\u044b \u043f\u043e\u043f\u0440\u043e\u0431\u0443\u0435\u043c \u043e\u0436\u0438\u0432\u0438\u0442\u044c \u0447\u0430\u0441\u0442\u0438\u0446\u0443 \u0432 \u043a\u043e\u0440\u043e\u0431\u043a\u0435 \u0441 \u043d\u0435\u043f\u0440\u043e\u043d\u0438\u0446\u0430\u0435\u043c\u044b\u043c\u0438 \u0441\u0442\u0435\u043d\u043a\u0430\u043c\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043c\u0435\u0442\u043e\u0434 \u041a\u0440\u0430\u043d\u043a\u0430 \u2014 \u041d\u0438\u043a\u043e\u043b\u0441\u043e\u043d\u0430. \u041d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0431\u0443\u0434\u0435\u0442 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440 \u03c8(x, t) \u043d\u0430 \u0432\u0441\u0435\u0445 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0448\u0430\u0433\u0430\u0445 \u043f\u043e \u0441\u0435\u0442\u043a\u0435, \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u0443\u044e \u0432\u043e\u043b\u043d\u043e\u0432\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u03c8(0) \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0441\u0440\u0435\u0437\u044b (N = 1000) \u0441 \u0434\u043b\u0438\u043d\u043e\u0439 \u0441\u0440\u0435\u0437\u0430 = L\/N.<\/p>\n<figure class=\"full-width\"><figcaption><\/figcaption><\/figure>\n<details class=\"spoiler\">\n<summary>\u0414\u043b\u0438\u043d\u043d\u0430\u044f \u043f\u0440\u043e\u0441\u0442\u044b\u043d\u044f \u0441 \u043a\u043e\u0434\u043e\u043c<\/summary>\n<div class=\"spoiler__content\">\n<pre><code class=\"python\">import numpy  as np from pylab import * from matplotlib import pyplot as plt from matplotlib import animation #matplotlib.use('GTK3Agg')   # from matplotlib import interactive # interactive(True)  ########################################Variables###################################################################################################### N_Slices = 1000            #Number of slices in the box  Time_step = 1e-18          #Time step for each iteration  Mass = 9.109e-31           #mass of electron  plank = 1.0546e-36         #Planks constant  L_Box = 1e-9           #Length of the box Grid = L_Box\/N_Slices                             #Lenght of each slice   #####################################Si(0) using the given equation ###############################################################################   Si_0 = np.zeros(N_Slices+1,complex)                        #Initiating Si funtion at time step = 0  x = np.linspace(0,L_Box,N_Slices+1)                             def G_Equation(x):     x_0 = L_Box\/2     Sig = 1e-10     k = 5e10     result  = exp(-(x-x_0)**2\/2\/Sig**2)*exp(1j*k*x)       #Given Equation at t = 0     return result Si_0[:] = G_Equation(x)                                     #Si funtion at time step = 0              #######################################V = Bxsi(0)################################################################################ a_1 = 1 + Time_step*plank*1j\/(2*Mass*(Grid**2))   #Diagonal of A Tridiagonal matrix a_2 = -Time_step*plank*1j\/(4*Mass*Grid**2)        #Up and Down to A Tridiagonal matrix b_1 =  1 - Time_step*plank*1j\/(2*Mass*(Grid**2))  #Diagonal of B Tridiagonal matrix b_2 =  Time_step*plank*1j\/(4*Mass*Grid**2)        #Up and Down to B Tridiagonal matrix    BxSi_0 = []                                                      #V = BxSi and si funtion at x = 0 for i in range(1000):     if i == 0:         BxSi_0.append(b_1*Si_0[0] + b_2*(Si_0[1]))                   #V can be maipulated by the equation in Text book               else:                                                              BxSi_0.append(b_1*Si_0[i] + b_2*(Si_0[i+1] + Si_0[i-1])) BxSi_0 = np.array(BxSi_0)  #####################################Tri Diagonal matrix algorithm#####################################################################################  def TDMAsolver(a, b, c, d):                                   #Instead of solving using Numpy.linalg, it is prefered to Use      nf = len(d)                                               #Tri Diagonal Matrix algorithm      ac, bc, cc, dc = map(np.array, (a, b, c, d))              # a,b,c's are up,dia,down element in tridiagonl matrix A     for it in range(1, nf):                                  #AX = d         mc = ac[it-1]\/bc[it-1]         bc[it] = bc[it] - mc*cc[it-1]          dc[it] = dc[it] - mc*dc[it-1]         \t         xc = bc     xc[-1] = dc[-1]\/bc[-1]      for il in range(nf-2, -1, -1):         xc[il] = (dc[il]-cc[il]*xc[il+1])\/bc[il]     return xc   global a                    #A matrix is fixed through out the problem, so it is good to globalize the variables  global b global c b = N_Slices*[a_1]          #In A matrix, Both  Up,Down elements are a_2 and diag matrix is a_1 a = (N_Slices-1)*[a_2] c = (N_Slices-1)*[a_2] ####################################Si 1st funtion solver####################################################################################  global Si_1                                 #First si_funtion usinf Axsi(0+h) = BxSi(0) Si_1 = TDMAsolver(a, b, c, BxSi_0)          #This can be solved by TDM(A,BxSi(0))   ###################################A funtion which caliculates si at each step##################################################################################### global Si_sd                            #AxSi_stepup = BxSi_stepdown Si_sd = {}                              #At first Buckting Si_stepdown in to directry which we can using for finding Si_stepup  def sifuntion(i):                       #In next iteration, Last iteration Si_stepup will be this iteration's Si_stepdown     if i == 0:         Si_sd[0] = Si_1         return Si_1     else:         Si_stepdown = Si_sd[i-1]         V = np.zeros(N_Slices,complex)         V[0] = b_1*Si_stepdown[0] + b_2*(Si_stepdown[1])         V[1:N_Slices-1] = b_1*Si_stepdown[1:N_Slices-1] + b_2*(Si_stepdown[2:N_Slices] + Si_stepdown[0:N_Slices-2])         V[N_Slices-1] = b_1*Si_stepdown[N_Slices-1]+ b_2*(Si_stepdown[N_Slices-2])         Si_stepup = TDMAsolver(a, b, c, V)         Si_sd[i] = Si_stepup          x = Si_stepup.real         return x ####################################Animating#######################################################################################       fig = plt.figure() ax = plt.axes(xlim=(0, 1000), ylim=(-1.5, 1.5)) line, = ax.plot([], [], lw=5) ax.legend(prop=dict(size=20)) ax.set_facecolor('black') ax.patch.set_alpha(0.8) ax.set_xlabel('$x$',fontsize = 15,color = 'blue') ax.set_ylabel(r'$|\\psi(x)|$',fontsize = 15,color = 'blue') ax.grid(color = 'blue') ax.set_title(r'$|\\psi(x)|$ vs $x$', color='blue',fontsize = 15 ) line, = ax.step([], [])  def init():     line.set_data([], [])     return line,   def animate(i):     x = np.linspace(0, 1000, num=1000)     y = sifuntion(i)     line.set_data(x, y)     line.set_color('red')     return line,  anim = animation.FuncAnimation(fig, animate, init_func=init,                                frames=10**5, interval=1, blit=True)#5*10**5  plt.vlines(1, -5, 5, linestyles = 'solid', color= 'green',lw=5) plt.vlines(999, -5, 5, linestyles = 'solid', color= 'green',lw=5) plt.text(1,1,'Boundary',rotation=90,color= 'green' ) plt.text(975,1,'Boundary',rotation=90,color= 'green' ) plt.figure(figsize=(10,10)) plt.show()     # Writer = animation.writers['ffmpeg'] # writer = Writer() # anim.save('im.mp4', writer=writer) <\/code><\/pre>\n<\/div>\n<\/details>\n<figure class=\"\"><figcaption><\/figcaption><\/figure>\n<p><a href=\"https:\/\/skillfactory.ru\/courses\/?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_ALLCOURSES&amp;utm_term=regular&amp;utm_content=290321\">\u0423\u0437\u043d\u0430\u0439\u0442\u0435<\/a>, \u043a\u0430\u043a \u043f\u0440\u043e\u043a\u0430\u0447\u0430\u0442\u044c\u0441\u044f \u0432 \u0434\u0440\u0443\u0433\u0438\u0445 \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u044f\u0445 \u0438\u043b\u0438 \u043e\u0441\u0432\u043e\u0438\u0442\u044c \u0438\u0445 \u0441 \u043d\u0443\u043b\u044f:<\/p>\n<ul>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/dstpro?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_DSPR&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Data Scientist<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/dataanalystpro?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_DAPR&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Data Analyst<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/dataengineer?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_DEA&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 \u043f\u043e Data Engineering<\/a><\/p>\n<\/li>\n<\/ul>\n<details class=\"spoiler\">\n<summary>\u0414\u0440\u0443\u0433\u0438\u0435 \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u0438 \u0438 \u043a\u0443\u0440\u0441\u044b<\/summary>\n<div class=\"spoiler__content\">\n<p><strong>\u041f\u0420\u041e\u0424\u0415\u0421\u0421\u0418\u0418<\/strong><\/p>\n<ul>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/python-fullstack-web-developer?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_FPW&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Fullstack-\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a \u043d\u0430 Python<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/java?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_JAVA&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f Java-\u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/java-qa-engineer?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_QAJA&amp;utm_term=regular&amp;utm_content=290321\">\u041f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u044f QA-\u0438\u043d\u0436\u0435\u043d\u0435\u0440 \u043d\u0430 JAVA<\/a><\/p>\n<\/li>\n<li>\n<p><a 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Learning&#187;<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/math-stat-for-ds#syllabus?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_MAT&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 &#171;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0434\u043b\u044f Data Science&#187;<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/math_and_ml?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_MATML&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 &#171;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 Machine Learning \u0434\u043b\u044f Data Science&#187;&nbsp;<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/skillfactory.ru\/python-for-web-developers?utm_source=infopartners&amp;utm_medium=habr&amp;utm_campaign=habr_PWS&amp;utm_term=regular&amp;utm_content=290321\">\u041a\u0443\u0440\u0441 &#171;Python \u0434\u043b\u044f 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