{"id":76833,"date":"2021-06-29T09:43:33","date_gmt":"2021-06-29T09:43:33","guid":{"rendered":"https:\/\/rubyskynews.com\/?p=76833"},"modified":"2021-06-29T09:43:33","modified_gmt":"2021-06-29T09:43:33","slug":"elektron-v-atome","status":"publish","type":"post","link":"https:\/\/rubyskynews.com\/index.php\/2021\/06\/29\/elektron-v-atome\/","title":{"rendered":"\u00a0 \u042d\u043b\u0435\u043a\u0442\u0440\u043e\u043d \u0432 \u0430\u0442\u043e\u043c\u0435."},"content":{"rendered":"<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div><p><strong><em>\u042d\u043b\u0435\u043a\u0442\u0440\u043e\u043d \u0432 \u0430\u0442\u043e\u043c\u0435.<\/em><\/strong>\u00a0 \u041e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0438\u0435 \u043d\u0430\u0433\u043b\u044f\u0434\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438 \u043c\u0438\u043a\u0440\u043e\u043e\u0431\u044a\u0435\u043a\u0442\u0430 \u043e\u0442\u043d\u044e\u0434\u044c \u043d\u0435 \u0438\u0441\u043a\u043b\u044e\u0447\u0430\u0435\u0442 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u0445 \u043e\u0431\u0440\u0430\u0437\u043e\u0432, \u0432\u043f\u043e\u043b\u043d\u0435 \u043f\u0440\u0438\u0433\u043e\u0434\u043d\u044b\u0445 \u0434\u043b\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043c\u0438\u043a\u0440\u043e\u043e\u0431\u044a\u0435\u043a\u0442\u0430 \u0432 \u0442\u0435\u0445 \u0438\u043b\u0438 \u0438\u043d\u044b\u0445 \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u0445. \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d \u0432 \u0430\u0442\u043e\u043c\u0435.<\/p>\n<p>\u041d\u0430\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u0430 \u0432 \u0430\u0442\u043e\u043c\u0435 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0430\u0431\u043e\u0440\u043e\u043c \u043a\u0432\u0430\u043d\u0442\u043e\u0432\u044b\u0445 \u0447\u0438\u0441\u0435\u043b: n, l, m, \u03c3. \u0414\u0430\u043d\u043d\u043e\u0435 \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0437\u0443\u0435\u0442\u0441\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u044d\u043d\u0435\u0440\u0433\u0438\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0432 \u0447\u0430\u0441\u0442\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0430\u0442\u043e\u043c\u0430 \u0432\u043e\u0434\u043e\u0440\u043e\u0434\u0430, \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u0447\u0438\u0441\u043b\u0430 n, \u0430 \u0432 \u0431\u043e\u043b\u0435\u0435 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u2013 \u043e\u0442 \u0447\u0438\u0441\u0435\u043b n \u0438 l. \u042d\u043b\u0435\u043a\u0442\u0440\u043e\u043d \u0432 \u0430\u0442\u043e\u043c\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0434\u0435\u043b\u043e\u043a\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u043d \u2013 \u0435\u0433\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0438\u043c\u0435\u044e\u0442 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u0432 \u0430\u0442\u043e\u043c\u0430. \u041e\u0431\u044b\u0447\u043d\u043e \u043f\u0440\u0438 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u0438\u0438 \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u0430 \u0432 \u0430\u0442\u043e\u043c\u0435 \u0432\u0432\u043e\u0434\u044f\u0442 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043e \u0442\u0430\u043a \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u043c <em>\u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e\u043c \u043e\u0431\u043b\u0430\u043a\u0435<\/em>, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043c\u043e\u0436\u043d\u043e \u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043a\u0430\u043a \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u0439 \u043e\u0431\u0440\u0430\u0437 \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u0430. \u0424\u043e\u0440\u043c\u0430 \u0438 \u044d\u0444\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u044b\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u044b \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e\u0433\u043e \u043e\u0431\u043b\u0430\u043a\u0430 \u0437\u0430\u0432\u0438\u0441\u044f\u0442 \u043e\u0442 \u043a\u0432\u0430\u043d\u0442\u043e\u0432\u044b\u0445 \u0447\u0438\u0441\u0435\u043b n, l, m \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u0435\u043d\u044f\u044e\u0442\u0441\u044f \u043e\u0442 \u043e\u0434\u043d\u043e\u0433\u043e \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u0430 \u0432 \u0430\u0442\u043e\u043c\u0435 \u043a \u0434\u0440\u0443\u0433\u043e\u043c\u0443.<\/p>\n<p>\u0427\u0442\u043e\u0431\u044b \u043e\u043f\u0438\u0441\u0430\u0442\u044c \u0440\u0430\u0437\u043c\u0435\u0440\u044b \u0438 \u0444\u043e\u0440\u043c\u0443 \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e\u0433\u043e \u043e\u0431\u043b\u0430\u043a\u0430, \u0432\u0432\u043e\u0434\u044f\u0442 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e<\/p>\n<p>u<sub>nlm<\/sub> (r, \u03b8, \u03c6) = v<sub>nl<\/sub> (r) Z<sub>lm<\/sub> (\u03b8, \u03c6),<\/p>\n<p>\u0433\u0434\u0435 r, \u03b8, \u03c6 \u2013 \u0441\u0444\u0435\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u0430. \u0424\u0443\u043d\u043a\u0446\u0438\u044e u<sub>nlm<\/sub> \u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0438\u0440\u0443\u044e\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c: u<sub>nlm<\/sub> (r, \u03b8, \u03c6) dV \u0435\u0441\u0442\u044c<em> \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c<\/em> \u043e\u0431\u043d\u0430\u0440\u0443\u0436\u0438\u0442\u044c \u0432 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0435 \u043e\u0431\u044a\u0435\u043c\u0430 dV \u0432\u0431\u043b\u0438\u0437\u0438 \u0442\u043e\u0447\u043a\u0438 (r, \u03b8, \u03c6) \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d, \u043d\u0430\u0445\u043e\u0434\u044f\u0449\u0438\u0439\u0441\u044f \u0432 \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0438 \u0441 \u043a\u0432\u0430\u043d\u0442\u043e\u0432\u044b\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438 n, l, m. \u0418\u043d\u0430\u0447\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, u<sub>nlm<\/sub> (r, \u03b8, \u03c6) \u0438\u043c\u0435\u0435\u0442 \u0441\u043c\u044b\u0441\u043b \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0439<em> \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438<\/em> \u043e\u0431\u043d\u0430\u0440\u0443\u0436\u0435\u043d\u0438\u044f \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u0430. \u041d\u0430\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e dV = r<sup>2<\/sup>drd\u03a9, \u0433\u0434\u0435 d\u03a9 = sin \u03b8d\u03b8d\u03c6 \u2013 \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u0442\u0435\u043b\u0435\u0441\u043d\u043e\u0433\u043e \u0443\u0433\u043b\u0430. \u0424\u0443\u043d\u043a\u0446\u0438\u044f<\/p>\n<p>w<sub>nl<\/sub> (r) dr = v<sub>nl<\/sub> (r) r<sup>2<\/sup> dr<\/p>\n<p>\u0435\u0441\u0442\u044c, \u0442\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043e\u0431\u043d\u0430\u0440\u0443\u0436\u0438\u0442\u044c \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d \u0441 \u043a\u0432\u0430\u043d\u0442\u043e\u0432\u044b\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438 n, l \u043d\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f\u0445 \u043e\u0442 \u044f\u0434\u0440\u0430, \u043f\u043e\u043f\u0430\u0434\u0430\u044e\u0449\u0438\u0445 \u0432 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043e\u0442 r \u0434\u043e r + dr.<\/p>\n<p>\u041f\u0440\u0438 l=0 (\u0442\u0430\u043a \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u044b\u0439 s-\u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d) \u0438\u043c\u0435\u0435\u043c \u0441\u0444\u0435\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e\u0435 \u043e\u0431\u043b\u0430\u043a\u043e. \u041f\u0440\u0438 l=1 (\u0440-\u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d) \u0438\u043c\u0435\u0435\u043c \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e\u0435 \u043e\u0431\u043b\u0430\u043a\u043e \u043b\u0438\u0431\u043e \u0432 \u0432\u0438\u0434\u0435 \u0441\u0432\u043e\u0435\u043e\u0431\u0440\u0430\u0437\u043d\u043e\u0433\u043e \u0432\u0435\u0440\u0435\u0442\u0435\u043d\u0430, \u043b\u0438\u0431\u043e \u0432 \u0432\u0438\u0434\u0435 \u0442\u043e\u0440\u043e\u0438\u0434\u0430, \u0447\u0442\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043a\u0432\u0430\u043d\u0442\u043e\u0432\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 m. \u0418\u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0441\u0435\u0431\u0435 \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d \u0432 \u0430\u0442\u043e\u043c\u0435, \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u0445 \u043e\u0431\u0440\u0430\u0437\u043e\u0432 \u043c\u043e\u0434\u0435\u043b\u044f\u043c\u0438 \u0448\u0430\u0440\u0430, \u0432\u0435\u0440\u0435\u0442\u0435\u043d\u0430, \u0442\u043e\u0440\u043e\u0438\u0434\u0430 \u0438 \u0442.\u0434.<\/p>\n<p>\u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u0430\u0442\u043e\u043c\u0430 \u0432\u043e\u0434\u043e\u0440\u043e\u0434\u0430 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0437\u0443\u0435\u0442\u0441\u044f \u0441\u0444\u0435\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u044b\u043c \u043e\u0431\u043b\u0430\u043a\u043e\u043c. \u0422\u0435\u043e\u0440\u0438\u044f \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u0447\u0442\u043e \u0432 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435<\/p>\n<p>w<sub>nl<\/sub> (r) = 4 r<sup>2 <\/sup>\/ r<sub>1<\/sub><sup>3\u00a0 <\/sup>exp (- 2r \/ r<sub>1<\/sub>).<\/p>\n<p>\u0425\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0437\u0443\u044e\u0449\u0438\u0439 \u044d\u0444\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u044b\u0439 \u0440\u0430\u0434\u0438\u0443\u0441 \u043e\u0431\u043b\u0430\u043a\u0430 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440 r<sub>1<\/sub> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435\u043c r<sub>1<\/sub> = h<sup>2<\/sup> \/ me<sup>2<\/sup> ; \u0432 \u0442\u0435\u043e\u0440\u0438\u0438 \u0411\u043e\u0440\u0430 \u043e\u043d \u0432\u044b\u0441\u0442\u0443\u043f\u0430\u043b \u043a\u0430\u043a \u0440\u0430\u0434\u0438\u0443\u0441 \u043f\u04355\u0440\u0432\u043e\u0439 \u043e\u0440\u0431\u0438\u0442\u044b.<\/p>\n<p>\u0412 \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435 \u0437\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u043f\u0440\u0438 \u043a\u0432\u0430\u043d\u0442\u043e\u0432\u044b\u0445 \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0430\u0445 \u0432 \u0430\u0442\u043e\u043c\u0435 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043d\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u044d\u043d\u0435\u0440\u0433\u0438\u0438, \u043d\u043e \u0438 \u0442\u0430\u043a\u0436\u0435 \u00ab\u043f\u0435\u0440\u0435\u0441\u0442\u0440\u043e\u0439\u043a\u0430\u00bb \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u044b\u0445 \u043e\u0431\u043b\u0430\u043a\u043e\u0432 \u2013 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0438\u0445 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u044b.<\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>","protected":false},"excerpt":{"rendered":"<p>\u042d\u043b\u0435\u043a\u0442\u0440\u043e\u043d \u0432 \u0430\u0442\u043e\u043c\u0435.\u00a0 \u041e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0438\u0435 \u043d\u0430\u0433\u043b\u044f\u0434\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438 \u043c\u0438\u043a\u0440\u043e\u043e\u0431\u044a\u0435\u043a\u0442\u0430 \u043e\u0442\u043d\u044e\u0434\u044c \u043d\u0435 \u0438\u0441\u043a\u043b\u044e\u0447\u0430\u0435\u0442 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u0445 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\u043d\u0430\u0431\u043e\u0440\u043e\u043c \u043a\u0432\u0430\u043d\u0442\u043e\u0432\u044b\u0445 \u0447\u0438\u0441\u0435\u043b: n, l, m, \u03c3. \u0414\u0430\u043d\u043d\u043e\u0435 \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0437\u0443\u0435\u0442\u0441\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u044d\u043d\u0435\u0440\u0433\u0438\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0432 \u0447\u0430\u0441\u0442\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0430\u0442\u043e\u043c\u0430 [&hellip;]<\/p>\n","protected":false},"author":1,"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":[52],"tags":[],"aioseo_notices":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u00a0 \u042d\u043b\u0435\u043a\u0442\u0440\u043e\u043d \u0432 \u0430\u0442\u043e\u043c\u0435. - Jobs\/ Internships\/ Scholarships\/<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/rubyskynews.com\/index.php\/2021\/06\/29\/elektron-v-atome\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" 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