{"id":31404,"date":"2024-08-31T04:40:18","date_gmt":"2024-08-31T04:40:18","guid":{"rendered":"https:\/\/science-hub.click\/%E7%90%83%E9%9D%A2%E8%AA%BF%E5%92%8C%E9%96%A2%E6%95%B0%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-08-31T04:40:18","modified_gmt":"2024-08-31T04:40:18","slug":"%E7%90%83%E9%9D%A2%E8%AA%BF%E5%92%8C%E9%96%A2%E6%95%B0%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=31404","title":{"rendered":"\u7403\u9762\u8abf\u548c\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p>\u6570\u5b66\u3067\u306f\u3001<b>\u7403\u9762\u8abf\u548c\u95a2\u6570<\/b>\u306f\u7279\u6b8a\u306a\u8abf\u548c\u95a2\u6570\u3067\u3059\u3002\u5ff5\u306e\u305f\u3081\u306b\u8a00\u3063\u3066\u304a\u304d\u307e\u3059\u304c\u3001\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u304c\u30bc\u30ed\u306e\u5834\u5408\u3001\u95a2\u6570\u306f\u8abf\u548c\u7684\u3067\u3042\u308b\u3068\u8a00\u308f\u308c\u307e\u3059\u3002\u7403\u9762\u8abf\u548c\u95a2\u6570\u306f\u3001\u56de\u8ee2\u306b\u95a2\u9023\u3059\u308b\u7279\u5b9a\u306e\u6f14\u7b97\u5b50\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u305f\u3081\u3001\u56de\u8ee2\u4e0d\u5909\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u306e\u306b\u7279\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p><p><span>\u6b21\u6570<\/span><span><i>l<\/i><\/span>\u306e\u8abf\u548c\u591a\u9805\u5f0f<span><i>P<\/i> ( <i>x<\/i> , <i>y<\/i> , <i>z<\/i> )<\/span>\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=20918\">\u6b21\u5143<\/a><\/span><span>2 <i>l<\/i> + 1<\/span>\u306e<span><a href=\"https:\/\/science-hub.click\/?p=5244\">\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<\/a><\/span>\u3092\u5f62\u6210\u3057\u3001<span><a href=\"https:\/\/science-hub.click\/?p=27928\">\u7403\u9762\u5ea7\u6a19<\/a><\/span>\u3067\u8868\u73fe\u3067\u304d\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {(  r,\\theta,\\varphi )} $$<\/div> <span>2 <i>l<\/i> + 1 \u306e<\/span>\u7d44\u307f\u5408\u308f\u305b\u3092\u4f7f\u7528: <\/p><center><div class=\"math-formual notranslate\">$$ {r^l \\cdot Y_{l,m}(\\theta, \\varphi)} $$<\/div> \u3001<\/center><p>\u3068<div class=\"math-formual notranslate\">$$ { &#8211; l \\le m \\le + l} $$<\/div> \u3002<\/p><p>\u7403\u9762\u5ea7\u6a19<div class=\"math-formual notranslate\">$$ {(  r,\\theta,\\varphi )} $$<\/div>\u306f\u305d\u308c\u305e\u308c\u3001\u7403\u306e\u4e2d\u5fc3\u304b\u3089\u306e\u8ddd\u96e2\u3001\u7def\u5ea6\u3001\u7d4c\u5ea6\u3067\u3059\u3002<\/p><p>\u540c\u6b21<span><a href=\"https:\/\/science-hub.click\/?p=35323\">\u591a\u9805\u5f0f<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=95765\">\u306f\u3059\u3079\u3066<\/a><\/span>\u3001\u5358\u4f4d\u7403<span><i>S<\/i> <sup>2<\/sup><\/span>\u3078\u306e\u5236\u9650\u306b\u3088\u3063\u3066\u5b8c\u5168\u306b\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002<\/p><div><p><strong><span><a href=\"https:\/\/science-hub.click\/?p=74671\">\u5b9a\u7fa9<\/a><\/span><\/strong><span>\u2014<\/span>\u8abf\u548c\u540c\u6b21\u591a\u9805\u5f0f\u306e\u5236\u9650\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u7403\u4e0a\u306e\u95a2\u6570\u306f\u7403\u9762\u8abf\u548c\u95a2\u6570\u3067\u3059\u3002<\/p><\/div><p>\u3053\u308c\u304c\u3001\u7814\u7a76\u3059\u308b\u554f\u984c\u306b\u3088\u3063\u3066<span><a href=\"https:\/\/science-hub.click\/?p=28052\">\u7570\u306a\u308b<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=34388\">\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f<\/a><\/span>\u306e\u52d5\u5f84\u90e8\u5206\u304c\u3053\u3053\u3067\u306f\u8868\u793a\u3055\u308c\u306a\u3044\u7406\u7531\u3067\u3059\u3002<\/p><p>\u7403\u9762\u8abf\u548c\u95a2\u6570\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=67593\">\u65b9\u5411<\/a><\/span>(\u7570\u65b9\u6027)\u3001\u3057\u305f\u304c\u3063\u3066\u56de\u8ee2 (\u76f4\u4ea4<span><a href=\"https:\/\/science-hub.click\/?p=30620\">\u5bfe\u79f0<\/a><\/span>\u7fa4<span><i>S<\/i> <i>O<\/i> (3)<\/span> ) \u306e\u6982\u5ff5\u304c\u767b\u5834\u3057\u3001\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u304c\u767b\u5834\u3059\u308b\u3068\u3059\u3050\u306b\u3001<span><a href=\"https:\/\/science-hub.click\/?p=66499\">\u6570\u7406<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=54039\">\u7269\u7406\u5b66<\/a><\/span>\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p><ul><li><span><a href=\"https:\/\/science-hub.click\/?p=44046\">\u97f3\u97ff\u5b66<\/a><\/span>\uff08\u8907\u6570\u306e\u30b9\u30d4\u30fc\u30ab\u30fc\u306b\u3088\u308b\u7a7a\u9593\u52b9\u679c\u306e\u518d\u69cb\u6210\uff09<\/li><li>\u30cb\u30e5\u30fc\u30c8\u30f3\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb<span><a href=\"https:\/\/science-hub.click\/?p=11998\">\u7406\u8ad6<\/a><\/span>\uff08\u9759\u96fb\u6c17\u5b66\u3001\u529b\u5b66\uff09\u3001\u91cd\u91cf\u6e2c\u5b9a\u306a\u3069\u3002<\/li><li>\u5730\u7403\u7269\u7406\u5b66 (<span><a href=\"https:\/\/science-hub.click\/?p=47664\">\u5730\u7403\u5100<\/a><\/span>\u306e\u8868\u73fe\u3001\u6c17\u8c61\u5b66)<\/li><li>\u7d44\u7e54\u306e<span><a href=\"https:\/\/science-hub.click\/?p=74501\">\u7d50\u6676\u5b66<\/a><\/span>\u3067\u306f\u3001<\/li><li><span><a href=\"https:\/\/science-hub.click\/?p=12092\">\u91cf\u5b50\u7269\u7406\u5b66<\/a><\/span>\uff08<span><a href=\"https:\/\/science-hub.click\/?p=20032\">\u6ce2\u52d5<\/a><\/span>\u95a2\u6570\u306e\u5c55\u958b\u3001\u96fb\u5b50<span><a href=\"https:\/\/science-hub.click\/?p=6160\">\u96f2<\/a><\/span>\u306e<span><a href=\"https:\/\/science-hub.click\/?p=37332\">\u5bc6\u5ea6<\/a><\/span>\u3001\u6c34\u7d20<span><a href=\"https:\/\/science-hub.click\/?p=33776\">\u539f\u5b50<\/a><\/span>\u306e\u539f\u5b50\u8ecc\u9053\u306e\u8a18\u8ff0\uff09<\/li><li>\u7b49<\/li><\/ul><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u7403\u9762\u8abf\u548c\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/O5DCmKrRsR8\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f<\/h2><p>\u6a5f\u80fd\u3092\u63a2\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {Y_{l,m}(\\theta, \\varphi)} $$<\/div>\u5358\u4e00\u5909\u6570\u306e 2 \u3064\u306e\u95a2\u6570\u306e\u7a4d\u306e\u5f62\u3067: <\/p><center><div class=\"math-formual notranslate\">$$ {Y_{l,m}(\\theta, \\varphi) = k P_{l,m}(\\cos \\theta) \\mathrm{e}^{+ \\, i \\, m \\, \\varphi} } $$<\/div><\/center><p>\u3053\u3053\u3067\u3001 <span><i>k \u306f<\/i><\/span>\u5b9a\u6570\u3067\u3042\u308a\u3001\u5f8c\u3067\u6b63\u898f\u5316\u306b\u3088\u3063\u3066\u4fee\u6b63\u3055\u308c\u307e\u3059\u3002\u56fa\u6709\u5024\u65b9\u7a0b\u5f0f\u306f\u3001\u95a2\u6570<span><i>P<\/i> <sub><i>l<\/i> , <i>m<\/i><\/sub> (cos\u03b8)<\/span>\u306e\u6b21\u6570 2 \u306e\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {- \\frac{1}{\\sin \\theta } \\frac{\\mathrm d ~}{\\mathrm d \\theta} \\left(\\sin \\theta \\frac{\\mathrm d P_{l,m}(\\cos \\theta)}{\\mathrm d \\theta}\\right) + \\frac{m^2}{\\sin^2 \\theta } P_{l,m}(\\cos \\theta)  = E_{l,m} P_{l,m}(\\cos \\theta) } $$<\/div><\/center><p>\u5909\u6570\u3092\u5909\u66f4\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\theta \\mapsto x = \\cos \\theta} $$<\/div>\u3053\u308c\u306f\u3001\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u306e\u4e00\u822c\u5316\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {- \\frac{\\mathrm d ~}{\\mathrm dx} \\left[ (1-x^2) \\frac{\\mathrm d P_{l,m}(x)}{\\mathrm dx}\\right] + \\frac{m^2}{(1-x^2) } P_{l,m}(x)  = E_{l,m} P_{l,m}(x) } $$<\/div><\/center><p>\u3053\u306e\u65b9\u7a0b\u5f0f\u306e\u56fa\u6709\u5024\u306f<span><i>m<\/i><\/span>\u306b\u4f9d\u5b58\u3057\u307e\u305b\u3093\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {E_{l,m}  = l (l+1)~} $$<\/div><\/center><p>\u56fa\u6709\u95a2\u6570<span><i>P<\/i> <sub><i>l<\/i> \u3001 <i>m<\/i><\/sub> ( <i>x<\/i> ) \u306f<\/span>\u3001 <span><i>m<\/i> = 0 \u306e<\/span>\u5834\u5408\u306b\u5bfe\u5fdc\u3059\u308b\u3001\u901a\u5e38\u306e\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u56fa\u6709\u95a2\u6570\u3067\u3042\u308b<span><a href=\"https:\/\/science-hub.click\/?p=40990\">\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0f<\/a><\/span><span><i>P<\/i> <sub><i>l<\/i><\/sub> ( <i>x<\/i> )<\/span>\u304b\u3089\u69cb\u7bc9\u3055\u308c\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {- \\frac{\\mathrm d ~}{\\mathrm dx} \\left[ (1-x^2) \\frac{\\mathrm d P_{l}(x)}{\\mathrm dx}\\right]   = l (l+1) P_{l}(x) } $$<\/div><\/center><p>\u30aa\u30ea\u30f3\u30c7\u30fb\u30ed\u30c9\u30ea\u30b2\u30b9\u306e\u751f\u6210\u516c\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {P_{l}(x) = \\frac{1}{2^l l\u00a0!} \\frac{\\mathrm d^l ~}{\\mathrm dx^l} \\left[ x^2 &#8211; 1  \\right]^l} $$<\/div><\/center><p>\u6b21\u306b\u3001\u6b21\u306e\u5f0f\u306b\u3088\u3063\u3066\u56fa\u6709\u95a2\u6570<span><i>P<\/i> <sub><i>l<\/i> , <i>m<\/i><\/sub> ( <i>x<\/i> )<\/span>\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {P_{l,m}(x) = (-1)^m \\left[ 1 &#8211; x^2 \\right]^{m\/2} \\frac{\\mathrm d^m P_{l}(x)}{\\mathrm dx^m} } $$<\/div><\/center><p>\u307e\u305f\u306f\u660e\u793a\u7684\u306b: <\/p><center><div class=\"math-formual notranslate\">$$ {P_{l,m}(x) = \\frac{(-1)^m}{2^l l\u00a0!} \\left[ 1 &#8211; x^2 \\right]^{m\/2} \\frac{\\mathrm d^{l+m} ~}{\\mathrm dx^{l+m}} \\left[ x^2 &#8211; 1  \\right]^l } $$<\/div><\/center><p>\u6ce8: \u5b9f\u969b\u306b\u306f\u3001\u6b21\u306e\u95a2\u6570<span><i>P<\/i> <sub><i>l<\/i> \u3001 <i>m<\/i><\/sub> ( <i>x<\/i> ) \u3092<\/span>\u8a08\u7b97\u3059\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ { m \\ge 0} $$<\/div>\u306a\u305c\u306a\u3089\u3001 <span><i>P<\/i> <sub><i>l<\/i> , <i>m<\/i><\/sub> ( <i>x<\/i> )<\/span>\u3068<span><i>P<\/i> <sub><i>l<\/i> , \u2212 <i>m<\/i><\/sub> ( <i>x<\/i> )<\/span>\u306e\u9593\u306b\u306f\u5358\u7d14\u306a\u95a2\u4fc2\u304c\u3042\u308b\u304b\u3089\u3067\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {P_{l,- \\, m}(x) = (-1)^m \\frac{(l-m) \\,\u00a0! }{(l +m) \\,\u00a0!} P_{l,m}(x)} $$<\/div><\/center><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u7403\u9762\u8abf\u548c\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/lJdo8UM_2eg\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u7403\u9762\u8abf\u548c\u95a2\u6570\u306e\u8868\u73fe<\/span><\/h3><p>\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u8868\u73fe\u3092\u899a\u3048\u308b\u7c21\u5358\u306a\u65b9\u6cd5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ { Y_{l,0} = P_l (\\cos \\theta)\\cdot \\sqrt{\\frac{2l+1}{4\\pi}}} $$<\/div> \u3001<\/center><p>\u3053\u3053\u3067\u3001 <span><i>P<\/i> <i>l<\/i> ( <i>x<\/i> ) \u306f<\/span>\u6b21\u6570<span><i>l<\/i><\/span>\u306e<span><a href=\"https:\/\/science-hub.click\/?p=24274\">\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0f<\/a><\/span>\u3067\u3059\u3002<\/p><p>\u6b21\u306b\u3001\u4ee5\u4e0b\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {J_+ Y_{l,m} = \\sqrt{(l^2-m^2)+(l-m)}\\cdot Y_{l,m+1}} $$<\/div><\/center><p>\u307e\u305f\u306f<\/p><center><div class=\"math-formual notranslate\">$$ { J_+ = e^{i\\phi}\\left( \\frac{\\partial}{\\partial \\theta} + \\frac{i}{\\tan \\theta}  \\cdot \\frac{\\partial}{\\partial \\phi}\\right)} $$<\/div><\/center><p>\u306f\u300c\u9ad8\u7d1a\u300d<span><a href=\"https:\/\/science-hub.click\/?p=21882\">\u6f14\u7b97\u5b50<\/a><\/span>\u3067\u3059\u3002<\/p><p>\u8ca0\u306e<span><i>m<\/i><\/span>\u306e\u5834\u5408\u3001 <div class=\"math-formual notranslate\">$$ {Y_{l,m} = (-1)^m.Y_{l, -m}^*} $$<\/div><\/p><p><i>\u6ce8:<\/i>\u79c1\u305f\u3061\u306f\u964d\u9806\u30b9\u30b1\u30fc\u30eb\u6f14\u7b97\u5b50\u306e\u5b58\u5728\u3092\u76f4\u89b3\u7684\u306b\u8a8d\u8b58\u3057\u3001\u5f97\u3089\u308c\u305f\u7d50\u679c\u306e\u4e00\u8cab\u6027\u3092\u30c1\u30a7\u30c3\u30af\u3067\u304d\u307e\u3059\u3002<\/p><p>\u591a\u304f\u306e\u5834\u5408\u3001\u3053\u306e\u6839\u62e0\u304c\u6ce8\u76ee\u3055\u308c\u307e\u3059<div class=\"math-formual notranslate\">$$ {|lm\\rangle} $$<\/div> :<\/p><p>\u3057\u305f\u304c\u3063\u3066\u3001\u7403<span><i>S<\/i> <sup>2<\/sup><\/span>\u4e0a\u306e\u4efb\u610f\u306e\u95a2\u6570\u3092\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {f(\\theta, \\phi) = f^{l,m}\\cdot |lm\\rangle} $$<\/div><\/center><p> (\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u7dcf\u548c\u898f\u5247\u306b\u304a\u3044\u3066)\u3001\u8907\u7d20\u4fc2\u6570<span><i>f<\/i> ( <i>l<\/i> , <i>m<\/i> )<\/span>\u306f\u3001\u6b21\u306e\u57fa\u790e\u306b\u304a\u3044\u3066<span><i>f<\/i><\/span>\u306e\u6210\u5206\u306e\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {|lm\\rangle} $$<\/div> (\u4e00\u822c\u5316\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570\u3068\u547c\u3076\u3053\u3068\u3082\u3042\u308a\u307e\u3059)\u3002<\/p><p><span><a href=\"https:\/\/science-hub.click\/?p=102393\">\u5316\u5b66<\/a><\/span>\u3084\u5730\u7403\u7269\u7406\u5b66\u3067\u306f\u3001\u300c\u5b9f\u969b\u306e\u300d\u7403\u9762\u8abf\u548c\u95a2\u6570\u3084\u5b9f\u969b\u306e\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u597d\u3080\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p><h3><span>\u6570\u5b66\u7684\u8868\u73fe<\/span><\/h3><p>\u5358\u4f4d\u7403\u4e0a\u306e\u76f4\u4ea4\u57fa\u5e95<span><a href=\"https:\/\/science-hub.click\/?p=56729\">\u3092\u5f62\u6210\u3059\u308b<\/a><\/span>\u7403\u9762\u8abf\u548c\u95a2\u6570\u3001\u4efb\u610f\u306e\u9023\u7d9a\u95a2\u6570<div class=\"math-formual notranslate\">$$ {f(\\theta, \\varphi)} $$<\/div>\u306f\u4e00\u9023\u306e\u7403\u9762\u8abf\u548c\u95a2\u6570\u306b\u5206\u89e3\u3055\u308c\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {f(\\theta, \\varphi) = \\sum_{l = 0}^{+\\infty} \\sum_{m = -l}^{+l} C_l^m \\cdot Y_l^m (\\theta , \\varphi)} $$<\/div><\/center><p>\u3053\u3053\u3067\u3001 <span><i>l<\/i><\/span>\u3068<span><i>m<\/i><\/span>\u306f\u6574\u6570\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3001 <span><i>C <sub>l<\/sub> <sup>m \u306f<\/sup><\/i><\/span>\u5b9a\u6570<span><a href=\"https:\/\/science-hub.click\/?p=99105\">\u4fc2\u6570<\/a><\/span>\u3067\u3042\u308a\u3001\u6570\u5b66\u3067\u306f\u591a\u304f\u306e\u5834\u5408\u3001\u3053\u306e\u57fa\u6570\u306b\u95a2\u9023\u3059\u308b\u4e00\u822c\u5316\u30d5\u30fc\u30ea\u30a8\u4fc2\u6570\u306e\u540d\u524d\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p><p>\u7403\u9762\u8abf\u548c\u95a2\u6570\u3067\u306e\u5c55\u958b\u306f\u3001\u89d2\u5ea6\u95a2\u6570\u306b\u9069\u7528\u3059\u308b\u3068\u3001\u5468\u671f\u95a2\u6570\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u3067\u306e\u5c55\u958b\u3068\u7b49\u4fa1\u3067\u3059\u3002<\/p><p> <span><i>Y <sub>l<\/sub> <sup>m \u306f<\/sup><\/i><\/span>\u8907\u7d20\u95a2\u6570<span><i><u>Y<\/u> <sub>l<\/sub> <sup>m<\/sup><\/i><\/span>\u306e\u5b9f\u90e8\u3067\u3059<\/p><center><div class=\"math-formual notranslate\">$$ {Y_l^m(\\theta , \\varphi) = \\operatorname{Re} \\left ( \\underline{Y_l^m}(\\theta , \\varphi) \\right )} $$<\/div><\/center><p> <span><i><u>Y<\/u> <sub>l<\/sub> <sup>m \u306f<\/sup><\/i><\/span>\u300c\u95a2\u9023\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u95a2\u6570\u300d\u3068\u547c\u3070\u308c\u3001\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\underline{Y_l^m}(\\theta , \\varphi) = \\sqrt{\\frac{2 \\cdot (l-m)!}{(l+m)!}} \\cdot P_l^m (\\cos \\theta) \\cdot e^{i m \\varphi}} $$<\/div><\/center><p>\u3053\u3053\u3067\u3001 <span><i>i<\/i><\/span>\u306f\u865a\u6570\u3001 <span><i>P <sub>l<\/sub> <sup>m \u306f<\/sup><\/i><\/span>\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0f\u3067\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {P_l^m (X) = \\frac{(-1)^m}{2^l \\cdot l!} \\cdot (1-X^2)^{m\/2} \\cdot  \\frac{\\partial^{m+l}}{\\partial X^{m+l}} \\left [ (X^2 &#8211; 1)^l \\right ]} $$<\/div><\/center><p>\u3057\u305f\u304c\u3063\u3066\u3001\u79c1\u305f\u3061\u306f<\/p><center><div class=\"math-formual notranslate\">$$ {Y_l^m(\\theta , \\varphi) = \\sqrt{\\frac{2 \\cdot (l-m)!}{(l+m)!}} \\cdot P_l^m (\\cos \\theta) \\cdot \\cos(m \\varphi)} $$<\/div><\/center><p>\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306a\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002 <\/p><ul><li><div class=\"math-formual notranslate\">$$ {P_0^0(\\cos \\theta) = 1} $$<\/div> ( <span><i>Y<\/i> <sub>0<\/sub> <sup>0 \u306f<\/sup><\/span>\u7b49\u65b9\u6027\u3067\u3059); <\/li><li><div class=\"math-formual notranslate\">$$ {P_1^0(\\cos \\theta) = \\cos \\theta} $$<\/div> ; <\/li><li><div class=\"math-formual notranslate\">$$ {P_1^1(\\cos \\theta) = &#8211; \\sin \\theta} $$<\/div> ; <\/li><li><div class=\"math-formual notranslate\">$$ {P_3^1(\\cos \\theta) = \\frac{3}{2} \\cdot \\sin \\theta \\cdot (-5 \\cdot \\cos^2 \\theta + 1)} $$<\/div> ;<\/li><\/ul><p>\u95a2\u6570<span><i>Y <sub>l<\/sub> <sup>m<\/sup><\/i> (\u03b8, \u03c6)<\/span>\u306f\u3001 <span><i>l \u304c<\/i><\/span>\u5897\u52a0\u3059\u308b<span><a href=\"https:\/\/science-hub.click\/?p=39804\">\u306b\u3064\u308c\u3066<\/a><\/span>\u307e\u3059\u307e\u3059\u5bfe\u79f0\u6027\u3092\u793a\u3057\u307e\u3059 (\u305f\u3060\u3057\u3001 <span><i>Y<\/i> <sub>0<\/sub> <sup>0<\/sup><\/span>\u306f\u5b9a\u6570\u95a2\u6570\u3067\u3042\u308a\u7403\u3092\u8868\u3059\u305f\u3081\u3001 <span><i>l<\/i> = 0 \u306e<\/span>\u5834\u5408\u3092\u9664\u304d\u307e\u3059)\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u7403\u9762\u8abf\u548c\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/WAsHNSvmU7Y\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0f<\/span><\/h3><p>\u5186\u5468\u8abf\u548c\u95a2\u6570\u306e\u5834\u5408\u3001\u4f59\u5f26\u95a2\u6570\u306e\u591a\u9805\u5f0f<span><i>P<\/i> <sub><i>l \u3092<\/i><\/sub><\/span>\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p><center> <span><i>Y<\/i> <sub><i>l<\/i><\/sub> (\u03b8) = <i>P<\/i> <sub><i>l<\/i><\/sub> (cos\u03b8)<\/span><\/center><p>\u4f7f\u7528\u3055\u308c\u308b\u591a\u9805\u5f0f<span><i>P<\/i> <sub><i>l \u306f<\/i><\/sub><\/span>\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb<sup>1<\/sup>\u591a\u9805\u5f0f\u3067\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {P_l(X) = \\frac{1}{2^l \\cdot l!} \\cdot \\frac{d^l}{d X^l}\\left [ (X^2 &#8211; 1)^l \\right ]} $$<\/div> (\u30b9\u30a4\u30b9\u306e\u6570\u5b66\u8005\u30ed\u30c9\u30ea\u30b2\u30b9\u306e\u516c\u5f0f)<\/center><p>\u4ee5\u4e0b\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <\/p><ul><li><div class=\"math-formual notranslate\">$$ {P_0(\\cos \\theta) = 1~} $$<\/div> (\u7b49\u65b9\u6027\u95a2\u6570); <\/li><li><div class=\"math-formual notranslate\">$$ {P_1(\\cos \\theta) = \\cos \\theta~} $$<\/div> ; <\/li><li><div class=\"math-formual notranslate\">$$ {P_2(\\cos \\theta) = \\frac{1}{2} (3 \\cos^2 \\theta -1)} $$<\/div> ; <\/li><li><div class=\"math-formual notranslate\">$$ {P_3(\\cos \\theta) = \\frac{1}{2} (5 \\cos^3 \\theta &#8211; 3 \\cos \\theta)} $$<\/div> ;<\/li><\/ul><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D8%AA%D9%88%D8%A7%D9%81%D9%82%D9%8A%D8%A7%D8%AA_%D9%83%D8%B1%D9%88%D9%8A%D8%A9\">\u062a\u0648\u0627\u0641\u0642\u064a\u0627\u062a \u0643\u0631\u0648\u064a\u0629 \u2013 arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/be.wikipedia.org\/wiki\/%D0%A1%D1%84%D0%B5%D1%80%D1%8B%D1%87%D0%BD%D1%8B%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%96\">\u0421\u0444\u0435\u0440\u044b\u0447\u043d\u044b\u044f \u0444\u0443\u043d\u043a\u0446\u044b\u0456 \u2013 bi\u00e9lorusse<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Harm%C3%B2nics_esf%C3%A8rics\">Harm\u00f2nics esf\u00e8rics \u2013 catalan<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/cs.wikipedia.org\/wiki\/Sf%C3%A9rick%C3%A9_harmonick%C3%A9_funkce\">Sf\u00e9rick\u00e9 harmonick\u00e9 funkce \u2013 tch\u00e8que<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/de.wikipedia.org\/wiki\/Kugelfl%C3%A4chenfunktionen\">Kugelfl\u00e4chenfunktionen \u2013 allemand<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Spherical_harmonics\">Spherical harmonics \u2013 anglais<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u7403\u9762\u8abf\u548c\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u7403\u9762\u8abf\u548c\u95a2\u6570\u306e\u6027\u8cea\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/u2KjspsM_i8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u6570\u5b66\u3067\u306f\u3001\u7403\u9762\u8abf\u548c\u95a2\u6570\u306f\u7279\u6b8a\u306a\u8abf\u548c\u95a2\u6570\u3067\u3059\u3002\u5ff5\u306e\u305f\u3081\u306b\u8a00\u3063\u3066\u304a\u304d\u307e\u3059\u304c\u3001\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u304c\u30bc\u30ed\u306e\u5834\u5408\u3001\u95a2\u6570\u306f\u8abf\u548c\u7684\u3067\u3042\u308b\u3068\u8a00\u308f\u308c\u307e\u3059\u3002\u7403\u9762\u8abf\u548c\u95a2\u6570\u306f\u3001\u56de\u8ee2\u306b\u95a2\u9023\u3059\u308b\u7279\u5b9a\u306e\u6f14\u7b97\u5b50\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u305f\u3081\u3001\u56de\u8ee2\u4e0d\u5909\u554f\u984c\u3092\u89e3 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":31405,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/u2KjspsM_i8\/0.jpg","fifu_image_alt":"\u7403\u9762\u8abf\u548c\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac","footnotes":""},"categories":[5],"tags":[11,13,14,10,12,8,32388,32386,16,15,9,32387],"class_list":["post-31404","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-techniques","tag-technologie","tag-news","tag-actualite","tag-dossier","tag-definition","tag-spherique","tag-harmonique-spherique","tag-sciences","tag-article","tag-explications","tag-harmonique"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/31404"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=31404"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/31404\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/31405"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=31404"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=31404"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=31404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}