[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/181358#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/181358","headline":"\u56fa\u6709\u72b6\u614b – Wikipedia","name":"\u56fa\u6709\u72b6\u614b – Wikipedia","description":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u56fa\u6709\u72b6\u614b”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082015\u5e747\u6708\uff09 \u91cf\u5b50\u529b\u5b66\u306b\u304a\u3044\u3066\u3001\u3042\u308b\u7269\u7406\u91cf A \u306e\u56fa\u6709\u72b6\u614b (\u82f1: eigenstate) \u3068\u306f\u3001\u305d\u306e\u7269\u7406\u91cf\uff08\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\uff09\u3092\u8868\u3059\u30a8\u30eb\u30df\u30fc\u30c8\u6f14\u7b97\u5b50 A^{displaystyle {hat {A}}} \u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb {|a1\u27e9,|a2\u27e9,\u2026}\u00a0{displaystyle","datePublished":"2022-03-27","dateModified":"2022-03-27","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki11\/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:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","height":"39","width":"50"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/181358","about":["Wiki"],"wordCount":4276,"articleBody":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u56fa\u6709\u72b6\u614b”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082015\u5e747\u6708\uff09\u91cf\u5b50\u529b\u5b66\u306b\u304a\u3044\u3066\u3001\u3042\u308b\u7269\u7406\u91cf A \u306e\u56fa\u6709\u72b6\u614b (\u82f1: eigenstate) \u3068\u306f\u3001\u305d\u306e\u7269\u7406\u91cf\uff08\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\uff09\u3092\u8868\u3059\u30a8\u30eb\u30df\u30fc\u30c8\u6f14\u7b97\u5b50 A^{displaystyle {hat {A}}}   \u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb {|a1\u27e9,|a2\u27e9,\u2026}\u00a0{displaystyle {|a_{1}rangle ,|a_{2}rangle ,ldots } } \u306e\u3053\u3068\u3067\u3042\u308b\u3002\u3088\u3063\u3066\u7269\u7406\u91cf A \u306e\u56fa\u6709\u72b6\u614b   {|a1\u27e9,|a2\u27e9,\u2026}\u00a0{displaystyle {|a_{1}rangle ,|a_{2}rangle ,ldots } } \u306f\u4ee5\u4e0b\u306e\u56fa\u6709\u5024\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3059\u3002A^|an\u27e9=an|an\u27e9(n=1,2,\u2026){displaystyle {hat {A}}|a_{n}rangle =a_{n}|a_{n}rangle quad (n=1,2,ldots )}\u4e00\u822c\u306b\u3001\u91cf\u5b50\u7cfb\u306b\u3064\u3044\u3066\u7269\u7406\u91cf\u306e\u6e2c\u5b9a\u3092\u884c\u3063\u305f\u6642\u3001\u3069\u3093\u306a\u306b\u540c\u3058\u3088\u3046\u306b\u72b6\u614b\u3092\u7528\u610f\u3057\u3066\u540c\u3058\u3088\u3046\u306b\u6e2c\u5b9a\u3092\u3057\u3066\u3082\u3001\u6e2c\u5b9a\u5024\u306f\u6e2c\u5b9a\u306b\u3088\u3063\u3066\u30d0\u30e9\u30d0\u30e9\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u7cfb\u304cA^{displaystyle {hat {A}}}\u306e\u56fa\u6709\u5024   an\u00a0{displaystyle a_{n} } \u306b\u5c5e\u3059\u308b\u56fa\u6709\u72b6\u614b |an\u27e9\u00a0{displaystyle |a_{n}rangle  } \u3067\u3042\u308b\u3068\u304d\u306f\u3001\u7269\u7406\u91cf A^{displaystyle {hat {A}}} \u3092\u89b3\u6e2c\u3059\u308c\u3070\u5fc5\u305a an\u00a0{displaystyle a_{n} } \u3068\u3044\u3046\u5024\u3092\u5f97\u308b\uff08\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u3092\u53c2\u7167\uff09\u3002\u3088\u3063\u3066\u300c\u7269\u7406\u91cf A^{displaystyle {hat {A}}} \u306e\u56fa\u6709\u72b6\u614b |an\u27e9\u00a0{displaystyle |a_{n}rangle  } \u306f\u3001\u7269\u7406\u91cf A^{displaystyle {hat {A}}} \u304c\u78ba\u5b9a\u3057\u305f\u5024 an{displaystyle a_{n}} \u3092\u6301\u3063\u3066\u3044\u308b\u72b6\u614b\u3067\u3042\u308b\u300d\u3068\u89e3\u91c8\u3067\u304d\u308b\u3002\u307e\u305f A^{displaystyle {hat {A}}} \u306f\u30a8\u30eb\u30df\u30fc\u30c8\u6f14\u7b97\u5b50\u306a\u306e\u3067\u3001\u305d\u306e\u56fa\u6709\u5024\u306f\u3059\u3079\u3066\u5b9f\u6570\u3067\u3042\u308b\u3002Table of Contents\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u72b6\u614b[\u7de8\u96c6]\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u72b6\u614b\u306e\u6642\u9593\u767a\u5c55[\u7de8\u96c6]\u540c\u6642\u56fa\u6709\u72b6\u614b[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u72b6\u614b[\u7de8\u96c6]\u5b9a\u5e38\u72b6\u614b\u306e\u30b7\u30e5\u30ec\u30c7\u30a3\u30f3\u30ac\u30fc\u65b9\u7a0b\u5f0f\u306f\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u8868\u3059\u6f14\u7b97\u5b50\u3067\u3042\u308b\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u56fa\u6709\u5024\u65b9\u7a0b\u5f0f\u3067\u3042\u308b\u3002H^|\u03c8\u27e9=E|\u03c8\u27e9{displaystyle {hat {H}}|psi rangle =E|psi rangle }\u3088\u3063\u3066\u305d\u306e\u89e3 |\u03c8\u27e9\u00a0{displaystyle |psi rangle  } \u306f\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u72b6\u614b\u3067\u3042\u308b\u3002\u56fa\u6709\u5024 E \u3092\u56fa\u6709\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u547c\u3076\u72b6\u614b\u304c\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u72b6\u614b\u306e\u3072\u3068\u3064 |\u03c8i\u27e9\u00a0{displaystyle |psi _{i}rangle  } \u3067\u3042\u3063\u305f\u5834\u5408\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6e2c\u5b9a\u3059\u308b\u3068\u3001\u6e2c\u5b9a\u5024\u306f |\u03c8i\u27e9\u00a0{displaystyle |psi _{i}rangle  } \u306b\u5bfe\u5fdc\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u5024 Ei \u304c\u5fc5\u305a\u5f97\u3089\u308c\u308b\u3002\u3088\u3063\u3066\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u72b6\u614b\u306f\u300c\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u78ba\u5b9a\u3057\u3066\u3044\u308b\u3088\u3046\u306a\u72b6\u614b\u300d\u3068\u3082\u8a00\u3048\u308b\u3002\u3042\u308b\u72b6\u614b\u30d9\u30af\u30c8\u30eb\u3084\u6ce2\u52d5\u95a2\u6570\u306e\u3053\u3068\u3092\u5358\u306b\u300c\u56fa\u6709\u72b6\u614b\u300d\u3068\u304b\u300c\u56fa\u6709\u95a2\u6570\u300d\u3068\u547c\u3076\u3053\u3068\u304c\u3042\u308b\u3002\u3057\u304b\u3057\u305d\u306e\u610f\u5473\u306f\u300c\u5b9a\u5e38\u72b6\u614b\u306e\u30b7\u30e5\u30ec\u30fc\u30c7\u30a3\u30f3\u30ac\u30fc\u65b9\u7a0b\u5f0f\u306e\u89e3\u3067\u3042\u308a\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u78ba\u5b9a\u3057\u3066\u3044\u308b\u3088\u3046\u306a\u7279\u5225\u306a\u72b6\u614b\u300d\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308a\u3001\u4efb\u610f\u306e\u72b6\u614b\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u3002\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u72b6\u614b\u306e\u6642\u9593\u767a\u5c55[\u7de8\u96c6]\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u72b6\u614b\u306e\u6642\u9593\u767a\u5c55\u306f\u3001\u6642\u9593\u4f9d\u5b58\u3059\u308b\u30b7\u30e5\u30ec\u30fc\u30c7\u30a3\u30f3\u30ac\u30fc\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u308b\u3068\u3001i\u210fddt|\u03c8\u27e9=H^|\u03c8\u27e9=E|\u03c8\u27e9{displaystyle ihbar {frac {d}{dt}}|psi rangle ={hat {H}}|psi rangle =E|psi rangle }\u3053\u306e\u89e3\u306f\u3001|\u03c8\u27e9=e\u2212iEt\/\u210f|\u03c8\u27e9{displaystyle |psi rangle =e^{-iEt\/hbar }|psi rangle }\u3088\u3063\u3066\u3001\u72b6\u614b\u30d9\u30af\u30c8\u30eb\u5168\u4f53\u306b\u304b\u304b\u308b\u4f4d\u76f8\u56e0\u5b50\u306f\u7269\u7406\u7684\u306b\u610f\u5473\u3092\u4e0e\u3048\u306a\u3044\u305f\u3081\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u72b6\u614b\u306f\u6642\u9593\u304c\u305f\u3063\u3066\u3082\u5909\u5316\u3057\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u540c\u6642\u56fa\u6709\u72b6\u614b[\u7de8\u96c6]2\u3064\u306e\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30ebA^{displaystyle {hat {A}}}\u3068B^{displaystyle {hat {B}}}\u304c\u4ea4\u63db\u3059\u308b\u3068\u304d\u3001\u3064\u307e\u308a[A^,B^]=0{displaystyle [{hat {A}},{hat {B}}]=0}\u306e\u3068\u304d\u306f\u3001A^{displaystyle {hat {A}}}\u3068B^{displaystyle {hat {B}}}\u306e\u3069\u3061\u3089\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3067\u3082\u3042\u308b\u30d9\u30af\u30c8\u30eb|A,B\u27e9{displaystyle |A,Brangle }\u304c\u5b58\u5728\u3059\u308b\u3002\u3053\u308c\u3092\u540c\u6642\u56fa\u6709\u72b6\u614b\uff08\u307e\u305f\u306f\u540c\u6642\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3001\u540c\u6642\u56fa\u6709\u95a2\u6570\uff09\u3068\u3044\u3046\u3002\u540c\u6642\u56fa\u6709\u72b6\u614b\u306f\u3001\u7269\u7406\u91cfA^{displaystyle {hat {A}}}\u3068B^{displaystyle {hat {B}}}\u306e\u4e21\u65b9\u304c\u78ba\u5b9a\u3057\u3066\u3044\u308b\u3088\u3046\u306a\u72b6\u614b\u3067\u3042\u308b\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/181358#breadcrumbitem","name":"\u56fa\u6709\u72b6\u614b – Wikipedia"}}]}]