[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/114955#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/114955","headline":"\u6b63\u6e96\u91cf\u5b50\u5316 – Wikipedia","name":"\u6b63\u6e96\u91cf\u5b50\u5316 – Wikipedia","description":"\u6b63\u6e96\u91cf\u5b50\u5316\uff08\u305b\u3044\u3058\u3085\u3093\u308a\u3087\u3046\u3057\u304b\u3001\u82f1: canonical quantization\uff09\u3068\u306f\u3001\u53e4\u5178\u529b\u5b66\u7684\u306a\u7406\u8ad6\u304b\u3089\u91cf\u5b50\u529b\u5b66\u7684\u306a\u7406\u8ad6\u3092\u63a8\u6e2c\u3059\u308b\u624b\u6cd5\uff08\u91cf\u5b50\u5316\uff09\u306e\u4e00\u7a2e\u3067\u3042\u308b\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30f3\u529b\u5b66(\u30cf\u30df\u30eb\u30c8\u30f3\u5f62\u5f0f\u306e\u53e4\u5178\u529b\u5b66)\u3067\u306e\u6b63\u6e96\u5909\u6570\u3092\u3001\u6b63\u6e96\u4ea4\u63db\u95a2\u4fc2\u3092\u307f\u305f\u3059\u3088\u3046\u306a\u30a8\u30eb\u30df\u30fc\u30c8\u6f14\u7b97\u5b50\u306b\u7f6e\u304d\u63db\u3048\u308b\u3002\u3053\u306e\u65b9\u6cd5\u3067\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30f3\u529b\u5b66\u306b\u304a\u3051\u308b\u30dd\u30a2\u30bd\u30f3\u62ec\u5f27\u304c\u3001\u91cf\u5b50\u529b\u5b66\u3067\u306e\u4ea4\u63db\u95a2\u4fc2\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u308b\u3002\u6b63\u6e96\u91cf\u5b50\u5316\u306b\u3088\u308a\u3001\u53e4\u5178\u529b\u5b66\u3067\u306f\u53ef\u63db\u3067\u3042\u3063\u305f\u529b\u5b66\u91cf(c-\u6570\u3001c\u306fclassical\u3092\u8868\u3059)\u306e\u306a\u3059\u4ee3\u6570\u306f\u3001\u91cf\u5b50\u529b\u5b66\u3067\u306f\u975e\u53ef\u63db\u306a\u529b\u5b66\u91cf(q-\u6570\u3001q\u306fquantum\u3092\u8868\u3059)\u306e\u306a\u3059\u4ee3\u6570\u306b\u79fb\u884c\u3059\u308b\u3002 \u6b63\u6e96\u91cf\u5b50\u5316\u3068\u306f\u3001\u91cf\u5b50\u529b\u5b66\u7684\u306a\u7cfb\u3092\u6271\u3046\u969b\u306b\u3001\u53e4\u5178\u529b\u5b66\u304b\u3089\u91cf\u5b50\u529b\u5b66\u3067\u306e\u5bfe\u5fdc\u5247\u3092\u69cb\u6210\u3059\u308b\u624b\u6cd5\u3067\u3042\u308b\u3002\u305d\u306e\u5177\u4f53\u7684\u306a\u624b\u7d9a\u304d\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u307e\u3068\u3081\u3089\u308c\u308b\u3002 Table of Contents \u6b63\u6e96\u91cf\u5b50\u5316\u306e\u624b\u7d9a\u304d[\u7de8\u96c6]1\u81ea\u7531\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]N\u81ea\u7531\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]1\u81ea\u7531\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]1\u6b21\u5143\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u306e\u5834\u5408\u306e\u4f8b[\u7de8\u96c6]\u53e4\u5178\u529b\u5b66\u3068\u306e\u5bfe\u5fdc[\u7de8\u96c6]\u4ea4\u63db\u95a2\u4fc2\u3068\u30dd\u30a2\u30bd\u30f3\u62ec\u5f27[\u7de8\u96c6]\u6b63\u6e96\u91cf\u5b50\u5316\u306b\u304a\u3051\u308b\u8af8\u554f\u984c[\u7de8\u96c6]\u7b2c\u4e8c\u91cf\u5b50\u5316[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6] \u6b63\u6e96\u91cf\u5b50\u5316\u306e\u624b\u7d9a\u304d[\u7de8\u96c6] \u5bfe\u8c61\u3068\u3059\u308b\u7cfb\u3092\u30cf\u30df\u30eb\u30c8\u30f3\u529b\u5b66(\u6b63\u6e96\u5f62\u5f0f)\u3067\u8a18\u8ff0\u3059\u308b\u3002 \u6b63\u6e96\u5f62\u5f0f\u306b\u304a\u3051\u308b\u6b63\u6e96\u5909\u6570 (q,p){displaystyle (q,,p)} \u3092\u3001\u6b63\u6e96\u4ea4\u63db\u95a2\u4fc2\u3092\u6e80\u305f\u3059\u6f14\u7b97\u5b50 (q^,p^){displaystyle ({hat {q}},{hat {p}})} \u306b\u7f6e\u304d\u63db\u3048\u308b\u3002 \u6b63\u6e96\u5909\u6570","datePublished":"2022-03-18","dateModified":"2022-03-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/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\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/7a3af5be78bd10ce541672755d4b824123e545c9","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/7a3af5be78bd10ce541672755d4b824123e545c9","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/114955","about":["Wiki"],"wordCount":6983,"articleBody":"\u6b63\u6e96\u91cf\u5b50\u5316\uff08\u305b\u3044\u3058\u3085\u3093\u308a\u3087\u3046\u3057\u304b\u3001\u82f1: canonical quantization\uff09\u3068\u306f\u3001\u53e4\u5178\u529b\u5b66\u7684\u306a\u7406\u8ad6\u304b\u3089\u91cf\u5b50\u529b\u5b66\u7684\u306a\u7406\u8ad6\u3092\u63a8\u6e2c\u3059\u308b\u624b\u6cd5\uff08\u91cf\u5b50\u5316\uff09\u306e\u4e00\u7a2e\u3067\u3042\u308b\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30f3\u529b\u5b66(\u30cf\u30df\u30eb\u30c8\u30f3\u5f62\u5f0f\u306e\u53e4\u5178\u529b\u5b66)\u3067\u306e\u6b63\u6e96\u5909\u6570\u3092\u3001\u6b63\u6e96\u4ea4\u63db\u95a2\u4fc2\u3092\u307f\u305f\u3059\u3088\u3046\u306a\u30a8\u30eb\u30df\u30fc\u30c8\u6f14\u7b97\u5b50\u306b\u7f6e\u304d\u63db\u3048\u308b\u3002\u3053\u306e\u65b9\u6cd5\u3067\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30f3\u529b\u5b66\u306b\u304a\u3051\u308b\u30dd\u30a2\u30bd\u30f3\u62ec\u5f27\u304c\u3001\u91cf\u5b50\u529b\u5b66\u3067\u306e\u4ea4\u63db\u95a2\u4fc2\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u308b\u3002\u6b63\u6e96\u91cf\u5b50\u5316\u306b\u3088\u308a\u3001\u53e4\u5178\u529b\u5b66\u3067\u306f\u53ef\u63db\u3067\u3042\u3063\u305f\u529b\u5b66\u91cf(c-\u6570\u3001c\u306fclassical\u3092\u8868\u3059)\u306e\u306a\u3059\u4ee3\u6570\u306f\u3001\u91cf\u5b50\u529b\u5b66\u3067\u306f\u975e\u53ef\u63db\u306a\u529b\u5b66\u91cf(q-\u6570\u3001q\u306fquantum\u3092\u8868\u3059)\u306e\u306a\u3059\u4ee3\u6570\u306b\u79fb\u884c\u3059\u308b\u3002\u6b63\u6e96\u91cf\u5b50\u5316\u3068\u306f\u3001\u91cf\u5b50\u529b\u5b66\u7684\u306a\u7cfb\u3092\u6271\u3046\u969b\u306b\u3001\u53e4\u5178\u529b\u5b66\u304b\u3089\u91cf\u5b50\u529b\u5b66\u3067\u306e\u5bfe\u5fdc\u5247\u3092\u69cb\u6210\u3059\u308b\u624b\u6cd5\u3067\u3042\u308b\u3002\u305d\u306e\u5177\u4f53\u7684\u306a\u624b\u7d9a\u304d\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u307e\u3068\u3081\u3089\u308c\u308b\u3002Table of Contents\u6b63\u6e96\u91cf\u5b50\u5316\u306e\u624b\u7d9a\u304d[\u7de8\u96c6]1\u81ea\u7531\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]N\u81ea\u7531\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]1\u81ea\u7531\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]1\u6b21\u5143\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u306e\u5834\u5408\u306e\u4f8b[\u7de8\u96c6]\u53e4\u5178\u529b\u5b66\u3068\u306e\u5bfe\u5fdc[\u7de8\u96c6]\u4ea4\u63db\u95a2\u4fc2\u3068\u30dd\u30a2\u30bd\u30f3\u62ec\u5f27[\u7de8\u96c6]\u6b63\u6e96\u91cf\u5b50\u5316\u306b\u304a\u3051\u308b\u8af8\u554f\u984c[\u7de8\u96c6]\u7b2c\u4e8c\u91cf\u5b50\u5316[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u6b63\u6e96\u91cf\u5b50\u5316\u306e\u624b\u7d9a\u304d[\u7de8\u96c6]\u5bfe\u8c61\u3068\u3059\u308b\u7cfb\u3092\u30cf\u30df\u30eb\u30c8\u30f3\u529b\u5b66(\u6b63\u6e96\u5f62\u5f0f)\u3067\u8a18\u8ff0\u3059\u308b\u3002\u6b63\u6e96\u5f62\u5f0f\u306b\u304a\u3051\u308b\u6b63\u6e96\u5909\u6570(q,p){displaystyle (q,,p)}\u3092\u3001\u6b63\u6e96\u4ea4\u63db\u95a2\u4fc2\u3092\u6e80\u305f\u3059\u6f14\u7b97\u5b50 (q^,p^){displaystyle ({hat {q}},{hat {p}})}\u306b\u7f6e\u304d\u63db\u3048\u308b\u3002\u6b63\u6e96\u5909\u6570(q,p){displaystyle (q,,p)}\u306e\u95a2\u6570\u3067\u3042\u308b\u53e4\u5178\u7684\u529b\u5b66\u91cfA(q,p){displaystyle A(q,,p)}\u306b\u3064\u3044\u3066\u3001\u6b63\u6e96\u5909\u6570\u306e\u9805\u30922\u3067\u5b9a\u3081\u305f\u6f14\u7b97\u5b50(q^,p^){displaystyle ({hat {q}},{hat {p}})}\u306b\u7f6e\u304d\u63db\u3048\u308b\u3002\u3053\u306e\u64cd\u4f5c\u306b\u3088\u3063\u3066\u3001\u53e4\u5178\u7684\u529b\u5b66\u91cfA=A(q,p){displaystyle A=A(q,,p)}\u306e\u91cf\u5b50\u529b\u5b66\u7684\u5bfe\u5fdc\u7269A^=A^(q^,p^){displaystyle {hat {A}}={hat {A}}({hat {q}},{hat {p}})}\u3092\u5b9a\u3081\u308b\u30022\u306e\u64cd\u4f5c\u3092\u3001\u3088\u308a\u8a73\u7d30\u306b\u8ff0\u3079\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u30021\u81ea\u7531\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]  \u53e4\u5178\u7684\u306a\u6b63\u6e96\u5909\u6570 (q,p){displaystyle (q,,p)}\u3092\u3001\u6b63\u6e96\u4ea4\u63db\u95a2\u4fc2[q^,p^]=i\u210f{displaystyle [{hat {q}},{hat {p}}]=ihbar }  \u3092\u307f\u305f\u3059\u6f14\u7b97\u5b50 (q^,p^){displaystyle ({hat {q}},{hat {p}})}\u306b\u7f6e\u304d\u63db\u3048\u308b\u3002N\u81ea\u7531\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]\u53e4\u5178\u7684\u306a\u6b63\u6e96\u5909\u6570 (q1,p1;q2,p2;\u22ef;qN,pN){displaystyle (q_{1},p_{1};q_{2},p_{2};cdots ;q_{N},p_{N})}\u3092\u3001\u6b63\u6e96\u4ea4\u63db\u95a2\u4fc2  [q^\u03b1,p^\u03b2]=i\u210f\u03b4\u03b1\u03b2{displaystyle [{hat {q}}_{alpha },{hat {p}}_{beta }]=ihbar delta _{alpha beta }}[q^\u03b1,q^\u03b2]=[p^\u03b1,p^\u03b2]=0\u03b1,\u03b2=1,\u2026,N{displaystyle [{hat {q}}_{alpha },{hat {q}}_{beta }]=[{hat {p}}_{alpha },{hat {p}}_{beta }]=0quad alpha ,beta =1,dots ,N}\u3092\u307f\u305f\u3059\u6f14\u7b97\u5b50\u306b\u7f6e\u304d\u63db\u3048\u308b\u3002\u6b63\u6e96\u91cf\u5b50\u5316\u306b\u304a\u3051\u308b\u6f14\u7b97\u5b50\u306e\u4e0d\u5b9a\u6027\u306a\u3069\u306e\u554f\u984c\u306b\u3064\u3044\u3066\u306f\u3001\u6b63\u6e96\u91cf\u5b50\u5316\u306b\u304a\u3051\u308b\u8af8\u554f\u984c\u306e\u9805\u3092\u53c2\u7167\u306e\u3053\u3068\u30021\u81ea\u7531\u5ea6\u306e\u5834\u5408[\u7de8\u96c6]1\u6b21\u5143\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u306e\u5834\u5408\u306e\u4f8b[\u7de8\u96c6]1\u6b21\u5143\u306e\u91cf\u5b50\u7cfb\u3092\u8003\u3048\u3001\u6ce2\u52d5\u95a2\u6570\u306e\u72b6\u614b\u7a7a\u9593\u3068\u3057\u3066\u3001\u5ea7\u6a19\u8868\u793a\u3057\u305f\u3082\u306e\u3092\u9078\u3076\u3002\u3059\u306a\u308f\u3061\u3001\u5ea7\u6a19x\u3068\u6642\u9593t\u306e\u95a2\u6570\u03c8(x,t){displaystyle psi (x,,t)}\u306e\u3046\u3061\u3001\u81ea\u4e57\u53ef\u7a4d\u5206\u306a\u3082\u306e\uff08\u5ea7\u6a19\u8868\u793a\u306e\u6ce2\u52d5\u95a2\u6570\uff09\u5168\u4f53\u304c\u3001\u7cfb\u306e\u30d2\u30eb\u30d9\u30eb\u30c8\u7a7a\u9593\u3092\u306a\u3059\u3002\u3053\u3053\u3067\u3001\u5ea7\u6a19x{displaystyle ,x}\u3068\u6b63\u6e96\u5171\u5f79\u904b\u52d5\u91cfpx{displaystyle ,p_{x}}\u3092\u3001x^\u03c8(x,t)=x\u03c8(x,t){displaystyle {hat {x}}psi (x,t)=xpsi (x,t)}p^x\u03c8(x,t)=\u2212i\u210f\u2202\u2202x\u03c8(x,t){displaystyle {hat {p}}_{x}psi (x,t)=-ihbar {frac {partial }{partial {}x}}psi (x,t)}\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u6f14\u7b97\u5b50x^{displaystyle {hat {x}}}\u3001p^x{displaystyle {hat {p}}_{x}}\u3067\u7f6e\u304d\u63db\u3048\u308b\u3002\u3053\u306e\u3068\u304d\u3001[x^,p^x]\u03c8(x,t)=i\u210f\u03c8(x,t){displaystyle [{hat {x}},{hat {p}}_{x}]psi (x,t)=ihbar psi (x,t)}\u3068\u306a\u308a\u3001x^{displaystyle {hat {x}}}\u3001p^x{displaystyle {hat {p}}_{x}}\u304c\u6b63\u6e96\u4ea4\u63db\u95a2\u4fc2\u3092\u307f\u305f\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u3064\u307e\u308a\u3001\u5ea7\u6a19\u8868\u793a\u3067\u306f\u639b\u3051\u7b97\u6f14\u7b97\u5b50\u3068\u3057\u3066\u306ex^{displaystyle {hat {x}}}\u3068\u5fae\u5206\u6f14\u7b97\u5b50\u3068\u3057\u3066\u306ep^x{displaystyle {hat {p}}_{x}}\u304c\u3001\u6b63\u6e96\u5909\u6570x,px{displaystyle x,,p_{x}}\u306e\u6b63\u6e96\u91cf\u5b50\u5316\u306b\u3088\u308b\u91cf\u5b50\u529b\u5b66\u7684\u8868\u73fe\u3068\u306a\u308b\u3002\u7cfb\u306e\u53e4\u5178\u529b\u5b66\u7684\u306a\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304cH(x,px)=px22m+V(x){displaystyle H(x,p_{x})={frac {p_{x}^{,2}}{2m}}+V(x)}\u3067\u4e0e\u3048\u3089\u308c\u308b\u3068\u3059\u308b\u3068\u3001\u6b63\u6e96\u91cf\u5b50\u5316\u306b\u3088\u308a\u3001\u91cf\u5b50\u529b\u5b66\u7684\u306a\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306fH^=H(x^,p^x)=\u2212\u210f22m\u22022\u2202x2+V(x){displaystyle {hat {H}}=H({hat {x}},{hat {p}}_{x})=-{frac {hbar ^{2}}{2m}}{frac {partial ^{2}}{partial x^{2}}}+V(x)}\u3068\u306a\u308b\u3002\u53e4\u5178\u529b\u5b66\u3068\u306e\u5bfe\u5fdc[\u7de8\u96c6]\u4ea4\u63db\u95a2\u4fc2\u3068\u30dd\u30a2\u30bd\u30f3\u62ec\u5f27[\u7de8\u96c6]\u6b63\u6e96\u91cf\u5b50\u5316\u306e\u64cd\u4f5c\u306f\u3001\u53e4\u5178\u529b\u5b66\u3067\u306e\u300c\u30dd\u30a2\u30bd\u30f3\u62ec\u5f27\u300d\u3068\u91cf\u5b50\u529b\u5b66\u306b\u304a\u3051\u308b\u300c\u4ea4\u63db\u95a2\u4fc2\u300d\u306e\u5bfe\u5fdc\u539f\u7406\u3092\u8003\u3048\u308b\u3068\u3001\u3088\u308a\u660e\u78ba\u306b\u306a\u308b\u3002{A,B}=\u2211\u03b1(\u2202A\u2202q\u03b1\u2202B\u2202p\u03b1\u2212\u2202B\u2202q\u03b1\u2202A\u2202p\u03b1)\u21d41i\u210f[A^,B^]=1i\u210f(A^B^\u2212B^A^){displaystyle {A,B}=sum _{alpha }left({frac {partial {}A}{partial {}q_{alpha }}}{frac {partial {}B}{partial {}p_{alpha }}}-{frac {partial {}B}{partial {}q_{alpha }}}{frac {partial {}A}{partial {}p_{alpha }}}right)Leftrightarrow {frac {1}{ihbar }}[{hat {A}},{hat {B}}]={frac {1}{ihbar }}left({hat {A}}{hat {B}}-{hat {B}}{hat {A}}right)}\u5b9f\u969b\u3001\u6b63\u6e96\u5909\u6570\u306b\u3064\u3044\u3066\u306f\u3001{q\u03b1,p\u03b2}=\u03b4\u03b1\u03b2\u21d4[q^\u03b1,p^\u03b2]=i\u210f\u03b4\u03b1\u03b2{displaystyle {q_{alpha },p_{beta }}=delta _{alpha beta }Leftrightarrow [{hat {q}}_{alpha },{hat {p}}_{beta }]=ihbar delta _{alpha beta }}{q\u03b1,q\u03b2}={p\u03b1,p\u03b2}=0\u21d4[q^\u03b1,q^\u03b2]=[p^\u03b1,p^\u03b2]=0{displaystyle {q_{alpha },q_{beta }}={p_{alpha },p_{beta }}=0Leftrightarrow [{hat {q}}_{alpha },{hat {q}}_{beta }]=[{hat {p}}_{alpha },{hat {p}}_{beta }]=0}\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3002\u529b\u5b66\u91cf\u306e\u6642\u9593\u767a\u5c55\u306b\u3064\u3044\u3066\u3082\u3001\u3053\u306e\u5bfe\u5fdc\u539f\u7406\u304b\u3089dAdt={A,H}+\u2202A\u2202t\u21d4dA^dt=1i\u210f[A^,H^]+\u2202A^\u2202t{displaystyle {frac {dA}{dt}}={A,H}+{frac {partial A}{partial t}}Leftrightarrow {frac {d{hat {A}}}{dt}}={frac {1}{ihbar }}[{hat {A}},{hat {H}}]+{frac {partial {hat {A}}}{partial t}}}\u3068\u30cf\u30a4\u30bc\u30f3\u30d9\u30eb\u30af\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u304c\u73fe\u308c\u308b\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u6b63\u6e96\u91cf\u5b50\u5316\u3067\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30f3\u529b\u5b66\u306b\u304a\u3051\u308b2\u3064\u306ec-\u6570\u306e\u529b\u5b66\u91cfA,B{displaystyle A,,B}\u306e\u6e80\u305f\u3059\u30dd\u30a2\u30bd\u30f3\u62ec\u5f27\u3092\u3001q-\u6570(\u6f14\u7b97\u5b50)\u306e\u529b\u5b66\u91cfA^,B^{displaystyle {hat {A}},,{hat {B}}}\u306e\u6e80\u305f\u3059\u4ea4\u63db\u95a2\u4fc2\u306b\u5bfe\u5fdc\u3055\u305b\u3001\u305d\u306e\u95a2\u4fc2\u3092\u901a\u3058\u3066\u91cf\u5b50\u529b\u5b66\u7684\u8868\u73fe\u3092\u5f97\u3066\u3044\u308b\u3068\u3082\u3044\u3048\u308b\u3002\u3053\u308c\u3089\u306e\u5bfe\u5fdc\u539f\u7406\u306f1925\u5e74\u306b\u30c7\u30a3\u30e9\u30c3\u30af\u306b\u3088\u3063\u3066\u660e\u3089\u304b\u306b\u3055\u308c\u305f\u3002\u6b63\u6e96\u91cf\u5b50\u5316\u306b\u304a\u3051\u308b\u8af8\u554f\u984c[\u7de8\u96c6]\u6b63\u6e96\u91cf\u5b50\u5316\u306f\u91cf\u5b50\u7cfb\u306b\u79fb\u884c\u3059\u308b\u4e00\u5b9a\u306e\u898f\u5247\u3092\u4e0e\u3048\u308b\u304c\u3001\u53e4\u5178\u7cfb\u306b\u304a\u3051\u308bc-\u6570\u306f\u53ef\u63db\u3067\u3042\u308b\u306e\u306b\u5bfe\u3057\u3001\u91cf\u5b50\u7cfb\u306eq-\u6570\u306f\u4e00\u822c\u306b\u975e\u53ef\u63db\u3068\u306a\u308a\u3001\u6f14\u7b97\u5b50\u306e\u7a4d\u306b\u3064\u3044\u3066\u306f\u9806\u5e8f\u306e\u4e0d\u5b9a\u6027\u304c\u6b8b\u308b\u3002\u307e\u305f\u3001\u91cf\u5b50\u5316\u5f8c\u306b\u30a8\u30eb\u30df\u30fc\u30c8\u6f14\u7b97\u5b50\u540c\u58eb\u306e\u7a4d\u306f\u30a8\u30eb\u30df\u30fc\u30c8\u6f14\u7b97\u5b50\u306b\u306f\u306a\u3089\u306a\u3044\u3002\u3053\u3046\u3057\u305f\u554f\u984c\u3092\u56de\u907f\u3059\u308b\u65b9\u6cd5\u3068\u3057\u3066\u3001\u30ef\u30a4\u30eb\u306e\u5bfe\u79f0\u5316\u6cd5(Weyl Calculus)\u3084\u7d4c\u8def\u7a4d\u5206\u91cf\u5b50\u5316\u7b49\u306e\u65b9\u6cd5\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\u3002\u307e\u305f\u6b63\u6e96\u91cf\u5b50\u5316\u3092\u3059\u308b\u306b\u306f\u3001\u305d\u306e\u7cfb\u306b\u5bfe\u5fdc\u3059\u308b\u6b63\u6e96\u5f62\u5f0f\u306e\u53e4\u5178\u529b\u5b66\u3092\u77e5\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u4e00\u65b9\u3067\u7d4c\u8def\u7a4d\u5206\u91cf\u5b50\u5316\u3067\u306f\u3001\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\u304c\u5206\u304b\u308c\u3070\u91cf\u5b50\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u7b2c\u4e8c\u91cf\u5b50\u5316[\u7de8\u96c6]\u91cf\u5b50\u529b\u5b66\u306b\u304a\u3051\u308b\u6b63\u6e96\u91cf\u5b50\u5316\u306e\u65b9\u6cd5\u306f\u7c92\u5b50\u306b\u5bfe\u3059\u308b\u91cf\u5b50\u5316\u3092\u4e0e\u3048\u308b\u304c\u3001\u5834\u306e\u91cf\u306b\u3064\u3044\u3066\u3082\u3001\u6b63\u6e96\u91cf\u5b50\u5316\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u5834\u306e\u91cf\u306b\u5bfe\u3059\u308b\u6b63\u6e96\u91cf\u5b50\u5316(\u7b2c\u4e8c\u91cf\u5b50\u5316)\u3067\u306f\u3001\u5834\u306e\u6f14\u7b97\u5b50\u03c6(t, x)\u3068\u5bfe\u5fdc\u3059\u308b\u6b63\u6e96\u904b\u52d5\u91cf\u03c0(t, x)\u306b\u5bfe\u3057\u3001\u540c\u6642\u523b\u3067\u306e\u6b63\u6e96\u4ea4\u63db\u95a2\u4fc2[\u03d5(t,x),\u03c0(t,y)]=i\u210f\u03b4(x\u2212y){displaystyle [phi (t,mathbf {x} ),pi (t,mathbf {y} )]=ihbar delta (mathbf {x} -mathbf {y} )}\u3092\u8ab2\u3059\u3053\u3068\u3067\u884c\u308f\u308c\u308b\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/114955#breadcrumbitem","name":"\u6b63\u6e96\u91cf\u5b50\u5316 – Wikipedia"}}]}]