[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/9585#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/9585","headline":"Baker-Campbell-Hauusdorff-formel  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Baker-Campbell-Hauusdorff-formel  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u6570\u5b66\u3067\u306f\u305d\u3046\u3067\u3059 Baker-Campbell-Hausdorff-formel \u6570\u5b66\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u305f\u65b9\u7a0b\u5f0f\u30d8\u30f3\u30ea\u30fc\u30fb\u30d5\u30ec\u30c7\u30ea\u30c3\u30af\u30fb\u30d9\u30a4\u30ab\u30fc\u3001\u30b8\u30e7\u30f3\u30fb\u30a8\u30c9\u30ef\u30fc\u30c9\u30fb\u30ad\u30e3\u30f3\u30d9\u30eb\u3001\u30d5\u30a7\u30ea\u30c3\u30af\u30b9\u30fb\u30cf\u30a6\u30b9\u30c9\u30eb\u30d5\u306f\u3001\u7279\u5b9a\u306e\u7dda\u5f62\u6f14\u7b97\u5b50\u306b\u4ea4\u63db\u6cd5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002 after-content-x4 \u306f \u30d0\u30c4 \u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u306e\u4e00\u5b9a\u306e\u7dda\u5f62\u6f14\u7b97\u5b50\u3001\u305d\u308c\u306f\u305d\u308c\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059 \u6307\u6570 \u3053\u306e\u6f14\u7b97\u5b50\u3092\u30b7\u30ea\u30fc\u30ba\u3068\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002 eX= \u2211k=0\u221e1k!Xk{displaystyle e^{x} = sum _ {k = 0}^{infty} {frac","datePublished":"2020-02-05","dateModified":"2020-02-05","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?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\/c19bb8d90896883a113259bfaddf3f6bdcc89047","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c19bb8d90896883a113259bfaddf3f6bdcc89047","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/9585","wordCount":3161,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u6570\u5b66\u3067\u306f\u305d\u3046\u3067\u3059 Baker-Campbell-Hausdorff-formel \u6570\u5b66\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u305f\u65b9\u7a0b\u5f0f\u30d8\u30f3\u30ea\u30fc\u30fb\u30d5\u30ec\u30c7\u30ea\u30c3\u30af\u30fb\u30d9\u30a4\u30ab\u30fc\u3001\u30b8\u30e7\u30f3\u30fb\u30a8\u30c9\u30ef\u30fc\u30c9\u30fb\u30ad\u30e3\u30f3\u30d9\u30eb\u3001\u30d5\u30a7\u30ea\u30c3\u30af\u30b9\u30fb\u30cf\u30a6\u30b9\u30c9\u30eb\u30d5\u306f\u3001\u7279\u5b9a\u306e\u7dda\u5f62\u6f14\u7b97\u5b50\u306b\u4ea4\u63db\u6cd5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u306f \u30d0\u30c4 \u30d0\u30ca\u30c3\u30cf\u30eb\u30fc\u30e0\u306e\u4e00\u5b9a\u306e\u7dda\u5f62\u6f14\u7b97\u5b50\u3001\u305d\u308c\u306f\u305d\u308c\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059 \u6307\u6570 \u3053\u306e\u6f14\u7b97\u5b50\u3092\u30b7\u30ea\u30fc\u30ba\u3068\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002 eX= \u2211k=0\u221e1k!Xk{displaystyle e^{x} = sum _ {k = 0}^{infty} {frac {1} {k\uff01}} x^{k}}} \u4e57\u7b97\u3068\u306f\u3001\u7d99\u627f\u3092\u610f\u5473\u3057\u3001\u95a2\u4fc2\u3059\u308b\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u3092\u8ffd\u52a0\u3059\u308b\u30dd\u30a4\u30f3\u30c8\u3092\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u30022\u3064\u306e\u7dda\u5f62\u6f14\u7b97\u5b50\u306e\u6574\u6d41\u5b50\uff08\u5618\u5618\u99ac\u8853\uff09 \u30d0\u30c4 \u3068 \u3068 \u3068\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4[ \u30d0\u30c4 \u3001 \u3068 ] \uff1a= \u30d0\u30c4 \u3068  –  \u3068 \u30d0\u30c4 {displaystyle [x\u3001y]\uff1a= xy-yx\u3001} \u5f7c\u306f\u53cc\u7dda\u5f62\u306e\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u3067\u3059\u3002\u5b9a\u7fa9\u304b\u3089\u3001Liesche Development\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u3068\u3082\u547c\u3070\u308c\u308b\u3044\u308f\u3086\u308bHadamard Lemma\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 eX\u3068 e\u2212X= \u2211m=0\u221e1m![ \u30d0\u30c4 \u3001 \u3068 ]m{displaystyle e^{x} ye^{ –  x} = sum _ {m = 0}^{infty} {frac {1} {m\uff01}} [x\u3001y] _ {m}} \u3068        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4[ \u30d0\u30c4 \u3001 \u3068 ] m= [ \u30d0\u30c4 \u3001 [ \u30d0\u30c4 \u3001 \u3068 ] m\u22121] {displaystyle [x\u3001y] _ {m} = [x\u3001[x\u3001y] _ {m-1}]\u3001} \u3068 [ \u30d0\u30c4 \u3001 \u3068 ] 0= \u3068 {displaystyle [x\u3001y] _ {0} = y\u3001} \u3002 \u6edd [ \u30d0\u30c4 \u3001 [ \u30d0\u30c4 \u3001 \u3068 ] ] = 0 {displaystyle [x\u3001[x\u3001y]] = 0\u3001} \u3068 [ \u3068 \u3001 [ \u3068 \u3001 \u30d0\u30c4 ] ] = 0 {displaystyle [y\u3001[y\u3001x]] = 0\u3001} \u3001 \u7533\u3057\u8fbc\u307f\u30b7\u30f3\u30d7\u30eb\u306aBaker-Campbell-Hausdorff\u5f0f eXeY= eYeXe[X,Y]{displaystyle e^{x} e^{y} = e^{y} e^{x} e^{[x\u3001y]}\u3001} eX+Y= eXeYe\u2212[X,Y]\/2{displaystyle e^{x+y} = e^{x} e^{y} e^{[x\u3001y]\/2}\u3001} \u3002 \u3069\u3061\u3089\u306e\u305f\u3081\u306b \u30d0\u30c4 {displaystyle x} \u3068 \u3068 {displaystyle y} \u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u306f\u975e\u5e38\u306b\u5e83\u7bc4\u3067\u3042\u308a\u3001\u552f\u4e00\u306e\u305f\u3081\u3067\u3059 \u30d0\u30c4 \u3001 \u3068 {displaystyle x\u3001y} \u306e\u74b0\u5883\u3067 0 {displaystyle 0} \u53ce\u675f\u3057\u307e\u3059\u3002\u305d\u3046\u3067\u3059 eXeY= eZ(X,Y){displaystyle e^{x} e^{y} = e^{z\uff08x\u3001y\uff09}\u3001} \u3068 Z(X,Y)=X+Y+12[X,Y]+112[X,[X,Y]]\u2212112[Y,[X,Y]]\u2212124[Y,[X,[X,Y]]]\u22121720([[[[X,Y],Y],Y],Y]+[[[[Y,X],X],X],X])+1360([[[[X,Y],Y],Y],X]+[[[[Y,X],X],X],Y])+1120([[[[Y,X],Y],X],Y]+[[[[X,Y],X],Y],X])+\u22ef{displaystyle {begin {aligned} z\uff08x\u3001y\uff09\uff06{} = x+y \\\uff06{}+{frac {1} {2}} [x\u3001y]+{frac {1} {12}} [x\u3001[x\u3001y]]  –  {frac {1} {12} {frac {1} {24}} [y\u3001[x\u3001[x\u3001y]]] \\\uff06{} quad- {frac {1} {720}}}\uff08[[[x\u3001y]\u3001y]\u3001y]\u3001y]\u3001y] +[[[[y\u3001x]\u3001x]\u3001x]\u3001x\uff09 [x\u3001y]\u3001y]\u3001y]\u3001x]+[[[[y\u3001x]\u3001x]\u3001x]\u3001y]\uff09\\\uff06{} quad+{frac {1} {120}}\uff08[[y\u3001x]\u3001y]\u3001x\u3001y]\u3001y]+[[[x\u3001y]\u3001x\u3001y]\u3001x\uff09 H.\u30d9\u30a4\u30ab\u30fc\uff1aProc Lond Math Soc\uff081\uff0934\uff081902\uff09347\u2013360;\u540c\u4e0a\uff081\uff0935\uff081903\uff09333\u2013374;\u540c\u4e0a\uff08Ser 2\uff093\uff081905\uff0924\u201347\u3002 J.\u30ad\u30e3\u30f3\u30d9\u30eb\uff1aProc Lond Math Soc 28\uff081897\uff09381\u2013390;\u540c\u4e0a29\uff081898\uff0914\u201332\u3002 L. Corwin\uff06F.P Greenleaf\uff1a \u30cb\u30eb\u30dd\u30fc\u30c6\u30f3\u5618\u5618\u30b0\u30eb\u30fc\u30d7\u3068\u305d\u306e\u5fdc\u7528\u306e\u8868\u73fe\u3001\u30d1\u30fc\u30c81\uff1a\u57fa\u672c\u7406\u8ad6\u3068\u4f8b \u3001\u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u5927\u5b66\u51fa\u7248\u5c40\u3001\u30cb\u30e5\u30fc\u30e8\u30fc\u30af\u30011990\u5e74\u3001ISBN 0-521-36034-X\u3002 E. B.\u30c0\u30a4\u30ca\u30ad\u30f3\uff1a Campbell-Hausdorff\u5f0f\u306e\u4fc2\u6570\u306e\u8a08\u7b97 \u3001\u6587\u66f8Akad Nauk Ussr\u300157\uff081947\uff09323\u2013326\u3002 \u30d6\u30e9\u30a4\u30a2\u30f3C.\u30db\u30fc\u30eb\uff1a \u5618\u306e\u30b0\u30eb\u30fc\u30d7\u3001\u5618\u4ee3\u6570\u3001\u304a\u3088\u3073\u8868\u73fe\uff1a\u57fa\u672c\u7684\u306a\u7d39\u4ecb \u3001\u30b9\u30d7\u30ea\u30f3\u30b0\u30b9\u30012003\u5e74\u3002ISBN0-387-40122-9\u3002 F. Hausdorff\uff1aBerl Hang Saeschen Akad Wiss Leipzig 58\uff081906\uff0919\u201348\u3002 W.\u30de\u30b0\u30ca\u30b9\uff1aComm Pur Appl Math VII\uff081954\uff09649\u2013673\u3002 W.\u30df\u30e9\u30fc\uff1a \u5bfe\u79f0\u30b0\u30eb\u30fc\u30d7\u3068\u305d\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3 \u3001\u30a2\u30ab\u30c7\u30df\u30c3\u30af\u30d7\u30ec\u30b9\u3001\u30cb\u30e5\u30fc\u30e8\u30fc\u30af\u30011972\u5e74\u3001S\u3002159\u2013161\u3002 ISBN 0-124-97460-0\u3002 H.\u30dd\u30a2\u30f3\u30ab\u30ec\uff1aCompt Renders Acad Sci Paris 128\uff081899\uff091065\u20131069; Camb Philos Trans 18\uff081899\uff09220\u2013255\u3002 M.W. Reinsch\uff1a \u30d9\u30a4\u30ab\u30fc\u30fb\u30ad\u30e3\u30f3\u30d7\u30d9\u30eb\u30fb\u30cf\u30a6\u30b9\u30c9\u30eb\u30d5\u30b7\u30ea\u30fc\u30ba\u306e\u7528\u8a9e\u306e\u5358\u7d14\u306a\u8868\u73fe \u3002 Jou Math Phys \u3001 41 \uff084\uff09\uff1a2434\u20132442\u3001\uff082000\uff09\u3002 doi\uff1a 10.1063\/1,533250 \uff08 arxiv preprint \uff09\uff09 W.\u30ed\u30b9\u30de\u30f3\uff1a \u5618\u30b0\u30eb\u30fc\u30d7\uff1a\u7dda\u5f62\u30b0\u30eb\u30fc\u30d7\u3092\u4ecb\u3057\u305f\u7d39\u4ecb \u3002\u30aa\u30c3\u30af\u30b9\u30d5\u30a9\u30fc\u30c9\u5927\u5b66\u51fa\u7248\u5c40\u30012002\u5e74\u3002 A.A. Sleog\uff06R.E\u3002 Walde\uff1a \u5618\u306e\u30b0\u30eb\u30fc\u30d7\u3068\u5618\u306e\u4ee3\u6570\u306e\u7d39\u4ecb \u3001\u30a2\u30ab\u30c7\u30df\u30c3\u30af\u30d7\u30ec\u30b9\u3001\u30cb\u30e5\u30fc\u30e8\u30fc\u30af\u30011973\u5e74\u3002ISBN0-12-614550-4\u3002 J.-P. Serre\uff1a \u4ee3\u6570\u3068\u5618\u306e\u30b0\u30eb\u30fc\u30d7 \u3001\u30d9\u30f3\u30b8\u30e3\u30df\u30f3\u30011965\u5e74\u3002 H. Kleinert\uff1a \u91cf\u5b50\u529b\u5b66\u3001\u7d71\u8a08\u3001\u30dd\u30ea\u30de\u30fc\u7269\u7406\u5b66\u3001\u304a\u3088\u3073\u91d1\u878d\u5e02\u5834\u306b\u304a\u3051\u308b\u30d1\u30b9\u7a4d\u5206 \u3001\u7b2c4\u7248\u3001 \u4e16\u754c\u79d1\u5b66\uff08\u30b7\u30f3\u30ac\u30dd\u30fc\u30eb\u30012006\u5e74\uff09 \uff08\u8aad\u307f\u3084\u3059\u3044 \u3053\u3053 \uff09\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/9585#breadcrumbitem","name":"Baker-Campbell-Hauusdorff-formel  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]