[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/14993#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/14993","headline":"\u671f\u5f85\u5024-Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","name":"\u671f\u5f85\u5024-Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 \u671f\u5f85\u5024 \uff08 \u5e73\u5747\u5024 \u3001 \u5e73\u5747 \u3001\u4ee5\u524d \u6570\u5b66\u7684\u5e0c\u671b \uff09 &#8211; \u30e9\u30f3\u30c0\u30e0\u30a8\u30af\u30b9\u30da\u30ea\u30a8\u30f3\u30b9\u306e\u671f\u5f85\u3055\u308c\u308b\u7d50\u679c\u3092\u6c7a\u5b9a\u3059\u308b\u5024\u3002\u671f\u5f85\u5024\u306f\u6700\u521d\u306e\u666e\u901a\u306e\u77ac\u9593\u3067\u3059\u3002\u6bcd\u96c6\u56e3\u306e\u7279\u5fb4\u306e\u4e88\u60f3\u5206\u5e03\u306e\u5024\u306e\u63a8\u5b9a\u91cf\u306f\u3001\u7b97\u8853\u5e73\u5747\u3067\u3059\u3002 after-content-x4 \u3082\u3057\u3082 \u30d0\u30c4 {displaystyle x} \u78ba\u7387\u7a7a\u9593\u306e\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3067\u3059 \uff08 \u304a\u304a \u3001","datePublished":"2021-03-28","dateModified":"2021-03-28","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/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\/68baa052181f707c662844a465bfeeb135e82bab","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/68baa052181f707c662844a465bfeeb135e82bab","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/14993","wordCount":5330,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u671f\u5f85\u5024 \uff08 \u5e73\u5747\u5024 \u3001 \u5e73\u5747 \u3001\u4ee5\u524d \u6570\u5b66\u7684\u5e0c\u671b \uff09 &#8211; \u30e9\u30f3\u30c0\u30e0\u30a8\u30af\u30b9\u30da\u30ea\u30a8\u30f3\u30b9\u306e\u671f\u5f85\u3055\u308c\u308b\u7d50\u679c\u3092\u6c7a\u5b9a\u3059\u308b\u5024\u3002\u671f\u5f85\u5024\u306f\u6700\u521d\u306e\u666e\u901a\u306e\u77ac\u9593\u3067\u3059\u3002\u6bcd\u96c6\u56e3\u306e\u7279\u5fb4\u306e\u4e88\u60f3\u5206\u5e03\u306e\u5024\u306e\u63a8\u5b9a\u91cf\u306f\u3001\u7b97\u8853\u5e73\u5747\u3067\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3082\u3057\u3082 \u30d0\u30c4 {displaystyle x} \u78ba\u7387\u7a7a\u9593\u306e\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3067\u3059 \uff08 \u304a\u304a \u3001 F\u3001 p \uff09\uff09 {displaystyle\uff08omega\u3001{mathcal {f}}\u3001mathbb {p}\uff09} \u5024\u304c\u3042\u308a\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4r \u3001 {displaystyle mathbb {r}\u3001} \u3053\u308c\u306f\u3001\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u306e\u671f\u5f85\u5024\u3067\u3059 \u30d0\u30c4 {displaystyle x} \u6570\u5b57\u3068\u547c\u3070\u308c\u307e\u3059 E\u30d0\u30c4 \uff1a= \u222b\u03a9\u30d0\u30c4 d P{displaystyle mathbb {e} x\uff1a= int limits _ {omega} xdmathbb {p}} [\u521d\u3081] \u305d\u308c\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u3064\u307e\u308a\u3001        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4E|\u30d0\u30c4 |= \u222b\u03a9|\u30d0\u30c4 |d P< + \u221e {displaystyle mathbb {e} | x | = int limits _ {omega} | x | dmathbb {p} \u3001 p n\u3001 {displaystyle p_ {1}\u3001p_ {2}\u3001dots\u3001p_ {n}\u3001} \u4e0a\u8a18\u306e\u5b9a\u7fa9\u304b\u3089\u3001\u671f\u5f85\u5024\u306e\u6b21\u306e\u5f0f\u304c \u3068 \u30d0\u30c4 {displaystyle mathbb {e} x} [3] \uff1a E\u30d0\u30c4 = \u2211i=1nxipi{displaystyle mathbb {e} x = sum _ {i = 1}^{n} x_ {i} p_ {i}} [4] \u3002 \u5909\u6570\u306e\u5834\u5408 \u30d0\u30c4 {displaystyle x} \u4e88\u60f3\u3055\u308c\u308b\u5024\u306e\u5f0f\u3067\u306f\u3001\u7121\u9650\u306b\u53d7\u3051\u5165\u308c\u307e\u3059\u304c\u3001\u30b3\u30f3\u30d0\u30fc\u30c6\u30a3\u3067\u591a\u304f\u306e\u5024\u3092\u53d7\u3051\u5165\u308c\u307e\u3059\u3002 \u221e {displaystyle infty} \u4ee3\u308f\u308a\u306b n {displaystyle n} \uff08\u3053\u306e\u30b7\u30ea\u30fc\u30ba\u304c\u7d76\u5bfe\u306b\u53ce\u675f\u3057\u3066\u3044\u308b\u5834\u5408\u306b\u306e\u307f\u5b58\u5728\u3057\u307e\u3059\uff09\u3002 \u3082\u3057\u3082 \u30d0\u30c4 {displaystyle x} \u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u6301\u3064\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3067\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 {displaystyle f\uff08x\uff09\u3001} \u3053\u308c\u304c\u671f\u5f85\u3055\u308c\u308b\u5024\u3067\u3059 E\u30d0\u30c4 = \u222b\u2212\u221e+\u221e \u30d0\u30c4 f \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 \u3002 {displaystyle mathbb {e} x = int limits _ { &#8211;  infty}^{+infty} \u301cxf\uff08x\uff09dx\u3002} \u3082\u3057\u3082 \u3068 = \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle y = varphi\uff08x\uff09} \u6e2c\u5b9a\u53ef\u80fd\u306a\u95a2\u6570\u3067\u3059 E\u3068 = E(\u03c6(X))= \u222bR \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 f \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 \u3002 {displaystyle mathbb {e} y = mathbb {e}\u5de6\uff08varphi\uff08x\uff09\u53f3\uff09= int limits _ {mathbb {r}} \u301cvarphi\uff08x\uff09f\uff08x\uff09dx\u3002}}} \u305d\u308c\u3089\u304c\u5b58\u5728\u3059\u308b\u5834\u5408 \u3068 \u30d0\u30c4 {displaystyle mathbb {e} x} \u3068 \u3068 \u3068 \u3001 {displaystyle mathbb {e} y\u3001} \u306b\uff1a Ec = c \u3001 {displaystyle mathbb {e} c = c\u3001} \u3069\u3053 c {displaystyle c} \u56fa\u5b9a\u95a2\u6570\u3067\u3059\uff08sum\/series\/Integral\u306e\u5747\u4e00\u6027\u306e\u7d50\u679c\uff09\u3001 \u2200a,bE\uff08 a \u30d0\u30c4 + b \uff09\uff09 = a E\u30d0\u30c4 + b {displaystyle forall _ {a\u3001b}; mathbb {e}\uff08ax+b\uff09= amathbb {e} x+b} \uff08Sum\/series\/Integral\u306e\u7dda\u5f62\u6027\u306e\u7d50\u679c\uff09\u3001 \u3082\u3057\u3082 \u30d0\u30c4 \u3001 \u3068 {displaystyle x\u3001y} \u5f7c\u3089\u306f\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059 E\uff08 \u30d0\u30c4 \u3068 \uff09\uff09 = E\u30d0\u30c4 E\u3068 \u3001 {displaystyle mathbb {e}\uff08xy\uff09= mathbb {e} xmathbb {e} y\u3001} \u3082\u3057\u3082 \u30d0\u30c4 \u2a7e 0 {displaystyle xgeqslant 0} \u307b\u307c\u3069\u3053\u3067\u3082\u3001\u305d\u308c E\u30d0\u30c4 \u2a7e 0 \u3001 {displaystyle mathbb {e} xgeqslant 0\u3001} E|\u30d0\u30c4 |\u2a7e |E\u30d0\u30c4 |\u3002 {displaystyle mathbb {e} | x | geqslant | mathbb {e} x |\u3002} \u671f\u5f85\u5024\u306e\u6982\u5ff5\u306f\u3001\u91cf\u5b50\u529b\u5b66\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u304c\u5bfe\u5fdc\u3059\u308b\u89b3\u5bdf\u306e\u671f\u5f85\u5024 A^{displaystyle {hat {a}}} \u6a19\u6e96\u5316\u3055\u308c\u305f\u6ce2\u52d5\u95a2\u6570\u3067\u8aac\u660e\u3055\u308c\u3066\u3044\u308b\u30b7\u30b9\u30c6\u30e0\u306e\u91cf\u5b50\u72b6\u614b\u306e\u5834\u5408 \u03c6 {displaystyle psi} \u5408\u8a08 \u27e8 A^\u27e9 \u03c8= \u222b \u03c6 \u2217\uff08 \u30d0\u30c4 \uff09\uff09 A^\uff08 \u30d0\u30c4 \u3001 \u2202 \/ \u2202 \u30d0\u30c4 \uff09\uff09 \u03c6 \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 \u3001 {displaystyle langle {hat {a}} rangle _ {psi} = int psi ^{*}\uff08x\uff09{hat {a}}\uff08x\u3001partial \/partial x\uff09psi\uff08x\uff09dx\u3001} \u7d71\u5408\u304c\u30b7\u30b9\u30c6\u30e0\u306e\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u5909\u6570\u5024\u3067\u5b9f\u884c\u3055\u308c\u308b\u5834\u5408\u3002 Diraca\u306e\u8868\u8a18\u3067\u306f\u3001\u3053\u306e\u30d1\u30bf\u30fc\u30f3\u3092\u4fdd\u5b58\u3067\u304d\u307e\u3059\u3002 \u27e8 A^\u27e9\u03c8= \u27e8 \u03c6 |A^|\u03c6 \u27e9 \u3002 {displaystyle langle {hat {a}} rank _ {psi} = langle psi | {hat {a}} | psi rangle\u3002}} \u671f\u5f85\u5024\u306e\u4e0d\u53ef\u89e3\u6027 A^\u3001 {displaystyle {hat {a}}\u3001} \u307e\u305f\u306f\u5206\u6563 A^\u3001 {displaystyle {hat {a}}\u3001} \u5408\u8a08 \uff08 d A^)2= \u27e8 A^2\u27e9  &#8211;  \u27e8 A^\u27e92\u3002 {displaystyle\uff08delta {hat {a}}\uff09^{2} = langle {hat {a}}^{2} rangle -langle {hat {a}} rangle^{2}\u3002} \u2191  J. J.  \u30e4\u30b3\u30d3\u30a2\u30f3  J. J. \u3001 R. R.  \u30b9\u30c6\u30f3\u30bb\u30eb  R. R. \u3001 \u78ba\u7387\u7406\u8ad6\u306e\u7d39\u4ecb \u3001\u30ef\u30eb\u30b7\u30e3\u30ef2010\u3001p\u300282  \u3002  \u2191  J. J.  \u30e4\u30b3\u30d3\u30a2\u30f3  J. J. \u3001 R. R.  \u30b9\u30c6\u30f3\u30bb\u30eb  R. R. \u3001 \u78ba\u7387\u7406\u8ad6\u306e\u7d39\u4ecb \u3001\u30ef\u30eb\u30b7\u30e3\u30ef2010\u3001p\u300281  \u3002  \u2191  \u671f\u5f85\u5024 \u3001 [\u306e\uff1a] PWN\u767e\u79d1\u4e8b\u5178 [\u30aa\u30f3\u30e9\u30a4\u30f3] [\u30a2\u30af\u30bb\u30b92021-07-22]  \u3002  \u2191  J. J.  \u30e4\u30b3\u30d3\u30a2\u30f3  J. J. \u3001 R. R.  \u30b9\u30c6\u30f3\u30bb\u30eb  R. R. \u3001 \u78ba\u7387\u7406\u8ad6\u306e\u7d39\u4ecb \u3001\u30ef\u30eb\u30b7\u30e3\u30ef2010\u3001p\u300285  \u3002  Jacek Jakubowski\u3001Rafa\u0142Szncelcel\uff1a \u78ba\u7387\u7406\u8ad6\u306e\u7d39\u4ecb \u3002\u30ef\u30eb\u30b7\u30e3\u30ef\uff1a\u30b9\u30af\u30ea\u30d7\u30c8\u30012004\u5e74\u3002ISBN 83-89716-01-1 \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\/wiki47\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/14993#breadcrumbitem","name":"\u671f\u5f85\u5024-Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178"}}]}]