[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki13\/archives\/202835#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki13\/archives\/202835","headline":"\u4f4d\u76f8\u306e\u305a\u308c – Wikipedia","name":"\u4f4d\u76f8\u306e\u305a\u308c – Wikipedia","description":"\u4f4d\u76f8\u306e\u305a\u308c\uff08\u4f4d\u76f8\u5dee\u3001\u4f4d\u76f8\u30b7\u30d5\u30c8\u3001\u30d5\u30a7\u30fc\u30ba\u30b7\u30d5\u30c8\uff09\u3068\u306f\u3001\u91cf\u5b50\u529b\u5b66\u306e\u6563\u4e71\u7406\u8ad6\u306b\u304a\u3044\u3066\u3001\u6563\u4e71\u306b\u3088\u3063\u3066\u5165\u5c04\u72b6\u614b\u3068\u6563\u4e71\u72b6\u614b\u306e\u9593\u306b\u751f\u3058\u308b\u4f4d\u76f8\u5dee\u306e\u3053\u3068\u3067\u3042\u308b\u3002 Table of Contents \u5165\u5c04\u72b6\u614b\u306e\u90e8\u5206\u6ce2\u5c55\u958b[\u7de8\u96c6]\u6563\u4e71\u72b6\u614b\u306e\u90e8\u5206\u6ce2\u5c55\u958b[\u7de8\u96c6]\u78ba\u7387\u306e\u4fdd\u5b58\u30fb\u4f4d\u76f8\u306e\u305a\u308c[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6] \u5165\u5c04\u72b6\u614b\u306e\u90e8\u5206\u6ce2\u5c55\u958b[\u7de8\u96c6] \u5165\u5c04\u5e73\u9762\u6ce2\u3092\u90e8\u5206\u6ce2\u5c55\u958b\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u305b\u308b\uff08\u30ec\u30a4\u30ea\u30fc\u306e\u516c\u5f0f\uff09\u3002 eik\u22c5r=\u2211l=0\u221e(2l+1)ilj(kr)Pl(cos\u2061\u03b8){displaystyle e^{imathbf {k} cdot mathbf {r} }=sum _{l=0}^{infty }(2l+1)i^{l}j(kr)P_{l}(cos theta )} \u3053\u308c\u306f r\u00a0{displaystyle","datePublished":"2022-03-31","dateModified":"2022-03-31","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki13\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki13\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/353ab5ed8763fadb41383c80ea01b6da488d3801","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/353ab5ed8763fadb41383c80ea01b6da488d3801","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki13\/archives\/202835","about":["Wiki"],"wordCount":4493,"articleBody":"\u4f4d\u76f8\u306e\u305a\u308c\uff08\u4f4d\u76f8\u5dee\u3001\u4f4d\u76f8\u30b7\u30d5\u30c8\u3001\u30d5\u30a7\u30fc\u30ba\u30b7\u30d5\u30c8\uff09\u3068\u306f\u3001\u91cf\u5b50\u529b\u5b66\u306e\u6563\u4e71\u7406\u8ad6\u306b\u304a\u3044\u3066\u3001\u6563\u4e71\u306b\u3088\u3063\u3066\u5165\u5c04\u72b6\u614b\u3068\u6563\u4e71\u72b6\u614b\u306e\u9593\u306b\u751f\u3058\u308b\u4f4d\u76f8\u5dee\u306e\u3053\u3068\u3067\u3042\u308b\u3002  Table of Contents\u5165\u5c04\u72b6\u614b\u306e\u90e8\u5206\u6ce2\u5c55\u958b[\u7de8\u96c6]\u6563\u4e71\u72b6\u614b\u306e\u90e8\u5206\u6ce2\u5c55\u958b[\u7de8\u96c6]\u78ba\u7387\u306e\u4fdd\u5b58\u30fb\u4f4d\u76f8\u306e\u305a\u308c[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u5165\u5c04\u72b6\u614b\u306e\u90e8\u5206\u6ce2\u5c55\u958b[\u7de8\u96c6]\u5165\u5c04\u5e73\u9762\u6ce2\u3092\u90e8\u5206\u6ce2\u5c55\u958b\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u305b\u308b\uff08\u30ec\u30a4\u30ea\u30fc\u306e\u516c\u5f0f\uff09\u3002  eik\u22c5r=\u2211l=0\u221e(2l+1)ilj(kr)Pl(cos\u2061\u03b8){displaystyle e^{imathbf {k} cdot mathbf {r} }=sum _{l=0}^{infty }(2l+1)i^{l}j(kr)P_{l}(cos theta )}\u3053\u308c\u306fr\u00a0{displaystyle r }\u304c\u975e\u5e38\u306b\u5927\u304d\u3044\u3068\u3053\u308d\u3067\u306f\u3001eik\u22c5r\u2192\u2211l=0\u221e(2l+1)2ik(eikrr\u2212(\u22121)le\u2212ikrr)Pl(cos\u2061\u03b8)(r\u2192\u221e)\u22ef(1){displaystyle e^{imathbf {k} cdot mathbf {r} }to sum _{l=0}^{infty }{frac {(2l+1)}{2ik}}({frac {e^{ikr}}{r}}-(-1)^{l}{frac {e^{-ikr}}{r}})P_{l}(cos theta )quad (rto infty )quad cdots (1)}\u6563\u4e71\u72b6\u614b\u306e\u90e8\u5206\u6ce2\u5c55\u958b[\u7de8\u96c6]\u6563\u4e71\u72b6\u614b\u306f\u3001\u5165\u5c04\u5e73\u9762\u6ce2\u3068\u6563\u4e71\u7403\u9762\u6ce2\u306e\u8db3\u3057\u3042\u308f\u305b\u3067\u3042\u308b\u3068\u8003\u3048\u308b\u3002  \u03c8+(r,\u03b8)=eik\u22c5r+f(\u03b8)eikrr\u22ef(2){displaystyle psi ^{+}(r,theta )=e^{imathbf {k} cdot mathbf {r} }+f(theta ){frac {e^{ikr}}{r}}quad cdots (2)}\u307e\u305f\u3001\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0fPl(cos\u2061\u03b8)\u00a0{displaystyle P_{l}(cos theta ) }\u306f\u5b8c\u5168\u7cfb\u3092\u306a\u3059\u3002\u222b0\u03c0Pl(cos\u2061\u03b8)Pl\u2032(cos\u2061\u03b8)sin\u2061\u03b8d\u03b8=22l+1\u03b4l,l\u2032{displaystyle int _{0}^{pi }P_{l}(cos theta )P_{l’}(cos theta )sin theta dtheta ={frac {2}{2l+1}}delta _{l,l’}}\u3088\u3063\u3066\u6563\u4e71\u632f\u5e45\u3092Pl(cos\u2061\u03b8)\u00a0{displaystyle P_{l}(cos theta ) }\u306e\u7dda\u5f62\u7d50\u5408\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u305d\u306e\u5c55\u958b\u4fc2\u6570\u3092al\u00a0{displaystyle a_{l} }\u3068\u3059\u308b\u3068\u3001f(\u03b8)=\u2211l=0\u221e(2l+1)2ikalPl(cos\u2061\u03b8)\u22ef(3){displaystyle f(theta )=sum _{l=0}^{infty }{frac {(2l+1)}{2ik}}a_{l}P_{l}(cos theta )quad cdots (3)}\u3088\u3063\u3066(2)\u5f0f\u306b(1)\u3001(3)\u5f0f\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001r\u00a0{displaystyle r }\u304c\u975e\u5e38\u306b\u5927\u304d\u3044\u3068\u3053\u308d\u3067\u306e\u6563\u4e71\u72b6\u614b\u03c8+(r,\u03b8)\u00a0{displaystyle psi ^{+}(r,theta ) }\u306f\u3001\u03c8+(r,\u03b8)\u2192\u2211l=0\u221e(2l+1)2ik[(1+al)eikrr\u2212(\u22121)le\u2212ikrr]Pl(cos\u2061\u03b8)(r\u2192\u221e)\u22ef(4){displaystyle psi ^{+}(r,theta )to sum _{l=0}^{infty }{frac {(2l+1)}{2ik}}{Big [}(1+a_{l}){frac {e^{ikr}}{r}}-(-1)^{l}{frac {e^{-ikr}}{r}}{Big ]}P_{l}(cos {theta })quad (rto infty )quad cdots (4)}\u3053\u306e\u62ec\u5f27\u5185\u306e\u7b2c\u4e00\u9805\u76ee\u306f\u5916\u5411\u304d\u7403\u9762\u6ce2\u3092\u3001\u7b2c\u4e8c\u9805\u76ee\u306f\u5185\u5411\u304d\u7403\u9762\u6ce2\u3092\u305d\u308c\u305e\u308c\u8868\u3057\u3066\u3044\u308b\u3002\u78ba\u7387\u306e\u4fdd\u5b58\u30fb\u4f4d\u76f8\u306e\u305a\u308c[\u7de8\u96c6]\u78ba\u7387\u306e\u4fdd\u5b58\u306b\u3088\u308a\u3001\u5916\u5411\u304d\u7403\u9762\u6ce2\u3068\u5185\u5411\u304d\u7403\u9762\u6ce2\u306e\u632f\u5e45\u306e\u7d76\u5bfe\u5024\u306f\u7b49\u3057\u304f\u306a\u3089\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002\u3064\u307e\u308a\u3001|1+al|=1{displaystyle left|1+a_{l}right|=1}\u3053\u3053\u3067\u4f4d\u76f8\u306e\u305a\u308c\u03b4l\u00a0{displaystyle delta _{l} }\uff08\u5b9f\u6570\u5024\uff09\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3059\u308b\u30021+al=ei2\u03b4l{displaystyle 1+a_{l}=e^{i2delta _{l}}}(1)\u5f0f\u3001(4)\u5f0f\u3092al\u00a0{displaystyle a_{l} }\u3067\u306f\u306a\u304f\u3001\u3053\u306e\u03b4l\u00a0{displaystyle delta _{l} }\u3092\u7528\u3044\u3066\u66f8\u304d\u76f4\u3059\u3068\u3001eik\u22c5r\u2192\u2211l=0\u221e(2l+1)krilsin\u2061(kr\u2212l\u03c02+\u03b4l)Pl(cos\u2061\u03b8)(r\u2192\u221e)\u22ef(1)\u2032{displaystyle e^{imathbf {k} cdot mathbf {r} }to sum _{l=0}^{infty }{frac {(2l+1)}{kr}}i^{l}sin(kr-{frac {lpi }{2}}+delta _{l})P_{l}(cos {theta })quad (rto infty )quad cdots (1)’}\u03c8+(r,\u03b8)\u2192\u2211l=0\u221e(2l+1)krei\u03b4lilsin\u2061(kr\u2212l\u03c02+\u03b4l)Pl(cos\u2061\u03b8)(r\u2192\u221e)\u22ef(4)\u2032{displaystyle psi ^{+}(r,theta )to sum _{l=0}^{infty }{frac {(2l+1)}{kr}}e^{idelta _{l}}i^{l}sin(kr-{frac {lpi }{2}}+delta _{l})P_{l}(cos {theta })quad (rto infty )quad cdots (4)’}\u3088\u3063\u3066\u6563\u4e71\u72b6\u614b\u306f\u5165\u5c04\u72b6\u614b\u3088\u308a\u4f4d\u76f8\u304c\u03b4l\u00a0{displaystyle delta _{l} }\u3060\u3051\u305a\u308c\u3066\u3044\u308b\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki13\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki13\/archives\/202835#breadcrumbitem","name":"\u4f4d\u76f8\u306e\u305a\u308c – Wikipedia"}}]}]