[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/17928#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/17928","headline":"Liouville\u5b9a\u7406\uff08\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u30e1\u30ab\u30cb\u30c3\u30af\uff09","name":"Liouville\u5b9a\u7406\uff08\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u30e1\u30ab\u30cb\u30c3\u30af\uff09","description":"before-content-x4 \u7269\u7406\u5b66\u3067\u306f\u3001 Teorema de Liouville \u3053\u308c\u306f\u3001\u6a5f\u68b0\u30b7\u30b9\u30c6\u30e0\u306e\u6642\u9593\u7684\u9032\u5316\u306b\u95a2\u3059\u308b\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u30e1\u30ab\u30cb\u30ba\u30e0\u306e\u7d50\u679c\u3067\u3059\u3002\u8fd1\u304f\u306e\u521d\u671f\u6761\u4ef6\u3092\u6301\u3064\u7c92\u5b50\u306e\u30bb\u30c3\u30c8\u306f\u3001\u4f4d\u76f8\u7a7a\u9593\u3067\u5360\u3081\u308b\u95a2\u9023\u9818\u57df\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5b9a\u7406\u306f\u3001\u5404\u7c92\u5b50\u304c\u9032\u5316\u3059\u308b\u306b\u3064\u308c\u3066\u4f38\u3073\u3066\u53ce\u7e2e\u3059\u308b\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u305d\u306e\u9818\u57df\u304c\u305d\u306e\u4f53\u7a4d\u3092\u7dad\u6301\u3059\u308b\u3053\u3068\u3092\u78ba\u7acb\u3057\u307e\u3059\u3002 after-content-x4 Table of Contents \u5e8f\u7ae0 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u76f4\u63a5\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5358\u7d14\u306a\u30d5\u30a9\u30fc\u30e0\u306b\u57fa\u3065\u304f\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 [","datePublished":"2019-08-20","dateModified":"2019-08-20","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/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\/320bb0b0467f9b3efe90ae582d21f808992d3cb6","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/320bb0b0467f9b3efe90ae582d21f808992d3cb6","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/17928","wordCount":2475,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u7269\u7406\u5b66\u3067\u306f\u3001 Teorema de Liouville \u3053\u308c\u306f\u3001\u6a5f\u68b0\u30b7\u30b9\u30c6\u30e0\u306e\u6642\u9593\u7684\u9032\u5316\u306b\u95a2\u3059\u308b\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u30e1\u30ab\u30cb\u30ba\u30e0\u306e\u7d50\u679c\u3067\u3059\u3002\u8fd1\u304f\u306e\u521d\u671f\u6761\u4ef6\u3092\u6301\u3064\u7c92\u5b50\u306e\u30bb\u30c3\u30c8\u306f\u3001\u4f4d\u76f8\u7a7a\u9593\u3067\u5360\u3081\u308b\u95a2\u9023\u9818\u57df\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5b9a\u7406\u306f\u3001\u5404\u7c92\u5b50\u304c\u9032\u5316\u3059\u308b\u306b\u3064\u308c\u3066\u4f38\u3073\u3066\u53ce\u7e2e\u3059\u308b\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u305d\u306e\u9818\u57df\u304c\u305d\u306e\u4f53\u7a4d\u3092\u7dad\u6301\u3059\u308b\u3053\u3068\u3092\u78ba\u7acb\u3057\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Table of Contents\u5e8f\u7ae0 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u76f4\u63a5\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5358\u7d14\u306a\u30d5\u30a9\u30fc\u30e0\u306b\u57fa\u3065\u304f\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 [ \u7de8\u96c6\u3057\u307e\u3059 ] Liouville\u65b9\u7a0b\u5f0f [ \u7de8\u96c6\u3057\u307e\u3059 ] \u91cf\u5b50\u529b\u5b66 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5e8f\u7ae0 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u305d\u306e\u8ecc\u8de1\u3092\u79fb\u52d5\u3059\u308b\u3053\u3068\u3067\u6642\u9593\u3068\u3068\u3082\u306b\u9032\u5316\u3059\u308b\u4f4d\u76f8\u7a7a\u9593\u306e\u9818\u57df\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u305d\u306e\u30dd\u30a4\u30f3\u30c8\u306e\u305d\u308c\u305e\u308c\u306f\u3001\u6642\u4ee3\u306b\u4f4d\u7f6e\u3059\u308b\u5730\u57df\u306b\u5909\u63db\u3055\u308c\u3001\u3055\u3089\u306b\u3001\u4f4d\u7f6e\u7a7a\u9593\u306e\u5225\u306e\u90e8\u5206\u306b\u3042\u308a\u307e\u3059\u3002 Liouville\u306e\u5b9a\u7406\u306f\u3001\u5f62\u5f0f\u306e\u7ffb\u8a33\u3068\u5909\u5316\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u3053\u306e\u5730\u57df\u306e\u5408\u8a08\u300c\u30dc\u30ea\u30e5\u30fc\u30e0\u300d\u306f\u4e0d\u5909\u306e\u307e\u307e\u3067\u3042\u308b\u3068\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u9818\u57df\u304c\u95a2\u9023\u3057\u3066\u3044\u308b\u5834\u5408\u306e\u6642\u9593\u7684\u9032\u5316\u306e\u9023\u7d9a\u6027\u306b\u3088\u308a\u3001\u6700\u521d\u306f\u5e38\u306b\u95a2\u9023\u3057\u7d9a\u3051\u307e\u3059\u3002 \u307b\u307c\u3059\u3079\u3066\u306e\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u4f4d\u76f8\u7a7a\u9593\u5185\u306e\u30dd\u30a4\u30f3\u30c8\u306e\u300c\u96f2\u300d\u306e\u6642\u9593\u7684\u9032\u5316\u304c\u3001\u5b9f\u969b\u306b\u306f\u3001\u305d\u306e\u96f2\u306e\u5f62\u72b6\u3068\u4f4d\u7f6e\u3092\u5909\u3048\u308b\u6a19\u6e96\u7684\u306a\u5909\u63db\u3067\u3042\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u3092\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u76f4\u63a5\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u4e00\u6642\u7684\u306a\u9032\u5316\u304c\u6a19\u6e96\u7684\u306a\u5909\u63db\u3067\u3042\u308a\u3001\u6bd4\u8f03\u7684\u5358\u7d14\u306a\u3082\u306e\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b1\u3064\u306e\u65b9\u6cd5\u3067\u3042\u308a\u3001\u305d\u3053\u304b\u3089\u306f\u4e0a\u8a18\u306e\u5ea7\u6a19\u5909\u5316\u306e\u6c7a\u5b9a\u8981\u56e0\u3092\u76f4\u63a5\u8a08\u7b97\u3057\u3001\u5b9f\u969b\u306b\u306f\u524d\u8ff0\u306e\u5909\u63db\u306e\u6c7a\u5b9a\u8981\u56e0\u304c1\u306b\u7b49\u3057\u3044\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002 \u5358\u7d14\u306a\u30d5\u30a9\u30fc\u30e0\u306b\u57fa\u3065\u304f\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5b9a\u7406\u3092\u30c6\u30b9\u30c8\u3059\u308b\u5225\u306e\u65b9\u6cd5\u306f\u3001\u4f53\u7a4d\u5f62\u72b6\u306b\u7559\u610f\u3059\u308b\u3053\u3068\u3067\u3059 \u03b7\u0393{displaystyle {eta} _ {gamma};} \u4f4d\u76f8\u7a7a\u9593\u306e\u3067\u3059 n  – \u5358\u7d14\u306a\u5f62\u5f0f\u306eTheimo\u7523\u7269\u3067\u3042\u308a\u3001Darboux\u306e\u5b9a\u7406\u306b\u6e96\u62e0\u3057\u3066\u3044\u308b\u306e\u306f\u3001\u6a19\u6e96\u7684\u306b\u5171\u5f79\u5909\u6570\u306e\u30da\u30a2\u306e\u7523\u7269\u3068\u3057\u3066\u8868\u3055\u308c\u307e\u3059\u3002 \u03b7\u0393= \u22c0i=1n\u304a\u304a = \u03c91\u2227 \u22ef \u2227 \u03c9n= d p1\u2227 \u22ef \u2227 d pn\u2227 d q1\u2227 \u22ef \u2227 d qn= d P1\u2227 \u22ef \u2227 d Pn\u2227 d Q1\u2227 \u22ef \u2227 d Qn{displaystyle {eta} _ {gamma} = bigwedge _ {i = 1}^{n} omega = omega _ {1} land dots land omega _ {n} = dp_ {1} land dots land dp_ {n} land dq_ {n} land dot dot dot dot dot dot dot dot dot dot dp {n} OTS\u30e9\u30f3\u30c9DP_ {n}\u571f\u5730dq_ {1}\u571f\u5730\u30c9\u30c3\u30c8\u30e9\u30f3\u30c9dq_ {n}}  \u305d\u306e\u5834\u5408\u3001\u5909\u63db\u306e\u6c7a\u5b9a\u8981\u56e0\u306f1\u306b\u7b49\u3057\u304f\u3001\u3057\u305f\u304c\u3063\u3066\uff1a        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u2200 \u306e \u2282 c \uff1a \u222bVdnqdnp= \u222b\u03d5\u03c4(V)dnQdnP{displaystyle forall vsubset\u30ac\u30f3\u30de\uff1aquad int _ {v} d ^ {n} {n} {n} {n} {n} {n} {n} mathbf {p} = int _ {tau} {q} d ^ {n} {n} mathbf {p}}}  \u3053\u306e\u6700\u5f8c\u306e\u8868\u73fe\u306f\u3001\u672c\u8cea\u7684\u306bLiouville\u306e\u5b9a\u7406\u306e\u58f0\u660e\u3067\u3059\u3002 Liouville\u65b9\u7a0b\u5f0f [ \u7de8\u96c6\u3057\u307e\u3059 ] Liouville\u306e\u5b9a\u7406\u306f\u3001\u30dd\u30a2\u30bd\u30f3\u306e\u30d6\u30e9\u30b1\u30c3\u30c8\u306e\u89b3\u70b9\u304b\u3089\u66f8\u304d\u76f4\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3068\u3057\u3066\u77e5\u3089\u308c\u308b\u3053\u306e\u4ee3\u66ff\u30d5\u30a9\u30fc\u30e0 Liouville\u65b9\u7a0b\u5f0f \u3001 \u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u307e\u3059\uff1a \u2202\u03c1\u2202t=  –  { r \u3001 h } {displaystyle {frac {partial rho} {partial t}} =  –  {\u3001rho\u3001h\u3001}}  \u307e\u305f\u306f\u306e\u89b3\u70b9\u304b\u3089 Liouville\u30aa\u30da\u30ec\u30fc\u30bf\u30fc \u3001\u300cliouvillian\u300d\u3068\u3082\u547c\u3070\u308c\u307e\u3059\uff1a L^= \u2211i=1d[\u2202H\u2202pi\u2202\u2202qi\u2212\u2202H\u2202qi\u2202\u2202pi]\u3001 {displaystyle {hat {mathbf {l}}} = sum _ {i = 1}^{d} left [{frac {partial h} {partial p_ {i}}}} {frac {partial} {partial q^{i}}}}}}}}-{{{partial f frac {partial f frac ac {partial} {partial p_ {i}}} right]\u3001}  \u305d\u308c\u306f\u5f62\u306b\u3064\u306a\u304c\u308a\u307e\u3059\uff1a \u2202\u03c1\u2202t+ L^r = 0\u3002 {displaystyle {frac {partial rho} {partial t}}+{hat {mathbf {l}}} rho = 0\u3002}  \u91cf\u5b50\u529b\u5b66 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u91cf\u5b50\u529b\u5b66\u3067\u306f\u3001\u6df7\u5408\u72b6\u614b\u306e\u9032\u5316\u3092\u8aac\u660e\u3059\u308bLiouville\u306e\u5b9a\u7406\u306b\u985e\u4f3c\u3057\u305f\u7d50\u679c\u304c\u3042\u308a\u307e\u3059\u3002\u5b9f\u969b\u3001\u5358\u7d14\u306a\u6a19\u6e96\u7684\u306a\u91cf\u5b50\u5316\u306b\u3088\u308a\u3001\u3053\u306e\u7d50\u679c\u306e\u6a5f\u68b0\u8f1d\u5ea6\u30d0\u30fc\u30b8\u30e7\u30f3\u306b\u5230\u9054\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u6b63\u5f0f\u306a\u624b\u9806\u3092\u9069\u7528\u3057\u3066\u3001Liouville\u306e\u5b9a\u7406\u306e\u91cf\u5b50\u985e\u4f3c\u4f53\u306b\u5230\u9054\u3057\u307e\u3059\u3002 \u2202\u2202tr =  –  i\u210f[ h \u3001 r ] {displaystyle {frac {partial} {partial t}} rho =  –  {frac {i} {hbar}} [h\u3001rho]}  \u3053\u3053\u3067\u3001\u03c1\u306f\u5bc6\u5ea6\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3067\u3059\u3002\u7d50\u679c\u304c\u89b3\u5bdf\u53ef\u80fd\u306a\u671f\u5f85\u5024\u306b\u9069\u7528\u3055\u308c\u308b\u3068\u3001ehrenfest\u306e\u5b9a\u7406\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u308b\u5bfe\u5fdc\u3059\u308b\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u5f62\u306b\u306a\u308a\u307e\u3059\u3002 ddt\u27e8 a \u27e9 = i\u210f\u27e8 [ h \u3001 a ] \u27e9 {displaystyle {frac {d} {dt}} langle arangle = {frac {i} {hbar}} langle [h\u3001a] rangle}  \u3069\u3053 a {displaystyle a\u3001} \u89b3\u5bdf\u53ef\u80fd\u3067\u3059\u3002           (adsbygoogle = window.adsbygoogle || 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