{"id":87829,"date":"2023-12-03T19:52:16","date_gmt":"2023-12-03T19:52:16","guid":{"rendered":"https:\/\/science-hub.click\/%E6%8B%AC%E5%BC%A7%E8%A1%A8%E8%A8%98%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2023-12-03T19:52:16","modified_gmt":"2023-12-03T19:52:16","slug":"%E6%8B%AC%E5%BC%A7%E8%A1%A8%E8%A8%98%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=87829","title":{"rendered":"\u62ec\u5f27\u8868\u8a18\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"
\n\"\"<\/figure>\u304b\u3089\u306e\u30a2\u30a4\u30c6\u30e0\u91cf\u5b50\u7269\u7406\u5b66<\/strong><\/small><\/td><\/tr>
\u91cf\u5b50\u8ad6<\/strong><\/small><\/td><\/tr>
\u91cf\u5b50\u96fb\u6c17\u529b\u5b66<\/small><\/td><\/tr>
\u91cf\u5b50\u529b\u5b66<\/small><\/td><\/tr>
\u5834\u306e\u7406\u8ad6<\/a><\/span><\/small><\/td><\/tr>
\u6a19\u6e96\u30e2\u30c7\u30eb<\/small><\/td><\/tr>
\u91cf\u5b50\u7d71\u8a08\u5b66<\/a><\/span><\/strong><\/small><\/td><\/tr>
\u30dc\u30fc\u30ba\u30fb\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3<\/small><\/td><\/tr>
\u30d5\u30a7\u30eb\u30df\u30fb\u30c7\u30a3\u30e9\u30c3\u30af<\/small><\/td><\/tr>
\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u30fb\u30dc\u30eb\u30c4\u30de\u30f3<\/small><\/td><\/tr>
\u7269\u7406\u5b66\u8005<\/strong><\/small><\/td><\/tr>
\u30dc\u30fc\u30a2\u30fb\u30c9\u30fb\u30d6\u30ed\u30a4<\/small><\/td><\/tr>
\u30dc\u30fc\u30ba\u30fb\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3<\/small><\/td><\/tr>
\u30d5\u30a7\u30eb\u30df – \u30c7\u30a3\u30e9\u30c3\u30af<\/small><\/td><\/tr>
\u30cf\u30a4\u30bc\u30f3\u30d9\u30eb\u30af – \u30d1\u30a6\u30ea<\/small><\/td><\/tr>
\u30b7\u30e5\u30ec\u30fc\u30c7\u30a3\u30f3\u30ac\u30fc – \u30d5\u30a1\u30a4\u30f3\u30de\u30f3<\/small><\/td><\/tr><\/table>

\u62ec\u5f27\u8868\u8a18\u306f\u3001<\/a><\/span><\/strong>\u91cf\u5b50\u529b\u5b66<\/a><\/span>\u306e\u65b9\u7a0b\u5f0f\u306e\u8a18\u8ff0\u3092\u5bb9\u6613\u306b\u3059\u308b\u305f\u3081\u3060\u3051\u3067\u306a\u304f\u3001\u91cf\u5b50\u72b6\u614b<\/span>\u3092\u8868\u3059\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5074\u9762\u3092\u5f37\u8abf\u3059\u308b\u305f\u3081\u306b\u3001\u30dd\u30fc\u30eb \u30c7\u30a3\u30e9\u30c3\u30af<\/a><\/span>\u306b\u3088\u3063\u3066\u5c0e\u5165\u3055\u308c\u307e\u3057\u305f (\u91cf\u5b50\u529b\u5b66<\/a><\/span>\u306e\u516c\u7406\u3092\u53c2\u7167)\u3002\u3053\u306e\u540d\u524d\u306f\u3001\u300c\u30d6\u30e9\u30b1\u30c3\u30c8\u306e\u30d6\u30e9\u30b1\u30c3\u30c8\u300d\u3092\u610f\u5473\u3059\u308b\u30d6\u30e9\u30b1\u30c3\u30c8<\/i>\u3068\u3044\u3046\u8a00\u8449\u904a\u3073\u306b\u7531\u6765\u3057\u3066\u3044\u307e\u3059\u3002

$$ {\\ \\langle\\} $$<\/div> ” \u305d\u3057\u3066 ”
$$ {\\ \\rangle\\} $$<\/div>\u305d\u308c\u305e\u308c\u300c\u30d6\u30e9\u300d\u3068\u300c\u30b1\u30c3\u30c8\u300d\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3053\u306e\u8868\u8a18\u6cd5\u306f\u305d\u308c\u4ee5\u6765\u3001\u4f5c\u7528\u7d20\u4ee3\u6570\u306e\u6570\u5b66\u7684\u7814\u7a76\u306b\u4f7f\u7528\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u306e\u5fdc\u7528\u5206\u91ce\u306f\u3088\u308a\u5e83\u304f\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>

\u300c\u30b1\u30c3\u30c8\u300d<\/span><\/h2>

\u610f\u5473<\/a><\/span><\/span><\/h3>

\u3092\u72b6\u614b\u7a7a\u9593\u306e\u30d9\u30af\u30c8\u30eb<\/a><\/span>\u3068\u3059\u308b\u3002\u6ce8\u76ee\u3055\u308c\u308b

$$ {\\left| u \\right\\rangle} $$<\/div>\u3053\u308c\u306f\u3001 Vector-ket<\/strong>\u307e\u305f\u306fket<\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>

2 \u3064\u306e\u30b1\u30c3\u30c8\u306f\u7dda\u5f62\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<\/a><\/span>\u3092\u5f62\u6210\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001 \u03bb 1<\/sub><\/span>\u3068\u03bb 2<\/sub><\/span>\u304c\u8907\u7d20\u6570\u306e\u5834\u5408\u3001 <\/p>

$$ {\\left| v \\right\\rangle = \\lambda_1 \\cdot \\left| u_1 \\right\\rangle + \\lambda_2 \\cdot \\left| u_2 \\right\\rangle} $$<\/div><\/dd><\/dl>

\u30b1\u30c3\u30c8\u3067\u3059\u3002<\/p>

\u3055\u3089\u306b\u9032\u3093\u3067\u3044\u304f\u3068\u3001

$$ {\\ |x\\rangle\\} $$<\/div>\u9023\u7d9a\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u4f9d\u5b58\u3059\u308b
$$ {\\ x\\} $$<\/div> \u3001\u305d\u3057\u3066\u3082\u3057
$$ {\\ f\\} $$<\/div>\u306f\u8907\u7d20\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001 <\/p>
$$ {\\left| u \\right\\rangle = \\int_{x_1}^{x_2}{f(x) \\cdot d{x}}} $$<\/div><\/dd><\/dl>

\u30b1\u30c3\u30c8\u3067\u3059\u3002<\/p>

\u30d7\u30ed\u30d1\u30c6\u30a3<\/span><\/h3>

2 \u3064\u306e\u30b1\u30c3\u30c8\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u306f<\/a><\/span>\u8907\u7d20\u6570\u3067\u3042\u308a\u3001\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\u3002

$$ {\\left( \\left| \\phi \\right\\rangle, \\left| \\psi \\right\\rangle \\right)} $$<\/div>\u3042\u308b\u3044\u306f\u3082\u3063\u3068\u5358\u7d14\u306b
$$ {\\left\\langle \\phi | \\psi \\right\\rangle} $$<\/div> \uff08\u4ee5\u4e0b\u3092\u53c2\u7167\uff1a\u30d6\u30e9\u30b8\u30e3\u30fc\uff09\u3002\u3053\u306e\u7a4d\u306f\u53cd\u7dda\u5f62\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6b21\u306e\u3053\u3068\u304c\u8a00\u3048\u307e\u3059\u3002 <\/p>
$$ {\\left\\langle \\phi | \\lambda \\cdot \\psi_1 + \\mu \\cdot \\psi_2 \\right\\rangle = \\lambda \\cdot \\left\\langle \\phi | \\psi_1 \\right\\rangle + \\mu \\cdot \\left\\langle \\phi | \\psi_2 \\right\\rangle} $$<\/div><\/dd><\/dl>

\u3057\u304b\u3057\u3001\u305d\u308c\u306f\uff1a <\/p>

$$ {\\left\\langle \\lambda \\cdot \\phi_1 + \\mu \\cdot \\phi_2 | \\psi \\right\\rangle = \\lambda^* \\cdot \\left\\langle \\phi_1 | \\psi \\cdot \\right\\rangle + \\mu^* \\cdot \\left\\langle \\phi_2 | \\psi \\right\\rangle} $$<\/div> \u3002<\/dd><\/dl>

(\u5f0f

$$ {\\ c^*\\} $$<\/div>\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u6b21\u306e\u5171\u5f79\u8907\u7d20\u6570\u3092\u53d6\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002
$$ {\\ c\\} $$<\/div> \u2014 \u8907\u7d20\u6570\u3092\u53c2\u7167)<\/p>

\u3053\u306e\u9078\u629e\u306b\u3088\u308a\u3001\u8907\u7d20\u6570\u306e\u30b9\u30ab\u30e9\u30fc<\/a><\/span>\u7a7a\u9593\u3067\u6b63\u3068\u306a\u308b\u30ce\u30eb\u30e0<\/a><\/span>\u306e\u5b9a\u7fa9\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u5b9f\u969b\u3001\u30d9\u30af\u30c8\u30eb\u81ea\u4f53\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u306f\u3001\u305d\u306e\u30ce\u30eb\u30e0\u306e2 \u4e57<\/a><\/span>\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {\\left\\langle \\lambda \\cdot \\psi | \\lambda \\cdot \\psi \\right\\rangle = \\lambda \\cdot \\lambda^* \\cdot \\left\\langle \\psi | \\psi \\right\\rangle = {\\left|\\lambda\\right|}^2 \\cdot \\left\\langle \\psi | \\psi \\right\\rangle} $$<\/div> \u3001<\/dd><\/dl>

\u3068

$$ {\\ \\lambda\\} $$<\/div>\u30b9\u30ab\u30e9\u30fc \u4e00\u7a2e\u306e\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u4fc2\u6570\u3002\u3057\u305f\u304c\u3063\u3066: <\/p>
$$ {\\left\\langle \\psi | \\psi \\right\\rangle = {\\left|\\left| \\psi \\right|\\right|}^2} $$<\/div><\/dd><\/dl>

\u30d9\u30fc\u30b9\u3068\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8<\/span><\/h3>

\u30d9\u30fc\u30b9\u3092\u4f7f\u7528\u3057\u3066\u30b1\u30c3\u30c8\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u3092\u5b9a\u7fa9\u3059\u308b\u3068\u4fbf\u5229\u3067\u3059\u3002\u3053\u308c\u306f\u30d9\u30af\u30c8\u30eb\u306e\u30bb\u30c3\u30c8<\/a><\/span>\u3067\u3059

$$ {\\left| u_n \\right\\rangle} $$<\/div> \u3001\u7dda\u5f62\u72ec\u7acb\u3002\u72b6\u614b\u7a7a\u9593\u306e\u6b21\u5143\u3068\u540c\u3058\u6570\u306e\u30d9\u30af\u30c8\u30eb\u304c\u5b58\u5728\u3057\u307e\u3059
$$ {\\ \\epsilon\\} $$<\/div> \u3001 \u305d\u3057\u3066
$$ {\\dim{\\left( \\epsilon \\right)} = N} $$<\/div> \u3002<\/p>

\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059

$$ {\\left| \\psi \\right\\rangle} $$<\/div>\u306e\u6839\u5143\u306b\u3042\u308b
$$ {\\left| u_n \\right\\rangle} $$<\/div> : <\/p>
$$ {\\left| \\psi \\right\\rangle = \\sum_{n = 1}^N {\\psi_n \\cdot \\left| u_n \\right\\rangle}} $$<\/div> \u3001<\/dd><\/dl>

\u307e\u305f\u306f

$$ {\\ \\psi_n\\} $$<\/div>\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8<\/i>\u3067\u3059
$$ {\\left| \\psi \\right\\rangle} $$<\/div>\u305d\u3057\u3066\u8907\u7d20\u6570\u306b\u5c5e\u3057\u307e\u3059\u3002<\/p>

\u901a\u5e38\u3001\u30b1\u30c3\u30c8\u306f\u3001\u5782\u76f4\u65b9\u5411\u306b\u914d\u7f6e\u3055\u308c\u305f\u4e00\u9023\u306e\u6570\u5024 (\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8) \u3067\u3042\u308b\u5217\u30d9\u30af\u30c8\u30eb<\/i>\u3068\u3057\u3066\u8868\u3055\u308c\u307e\u3059\u3002 <\/p>

$$ {\\left| \\psi \\right\\rangle = \\begin{pmatrix} \\psi_1 \\\\ \\psi_2 \\\\ \\vdots \\\\ \\psi_N \\end{pmatrix}_{\\epsilon} = \\begin{bmatrix} \\psi_1 \\\\ \\psi_2 \\\\ \\vdots \\\\ \\psi_N \\end{bmatrix} \\cdot \\begin{bmatrix} \\left| u_1 \\right\\rangle & \\left| u_2 \\right\\rangle & \\cdots & \\left| u_N \\right\\rangle \\end{bmatrix}} $$<\/div><\/dd><\/dl>
\n\"\u62ec\u5f27\u8868\u8a18\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u300c\u30d6\u30e9\u300d<\/span><\/h2>

\u610f\u5473<\/span><\/h3>

\u7a7a\u9593\u306e\u5404\u30b1\u30c3\u30c8\u3068\u95a2\u9023\u4ed8\u3051\u305f\u3044

$$ {\\ \\epsilon\\} $$<\/div> \u3001\u8907\u7d20\u6570\u3002\u3053\u306e\u305f\u3081\u306b\u3001\u7dda\u5f62\u95a2\u6570\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002
$$ {\\ \\chi\\} $$<\/div>\u306e\u3088\u3046\u306a \uff1a <\/p>
$$ {\\chi\u00a0: \\left| \\psi \\right\\rangle \\rightarrow \\lambda = \\chi(\\psi)} $$<\/div> \u3001 \u305d\u3057\u3066<\/dd>
$$ {\\chi{\\left( \\lambda_1 \\cdot \\left| \\psi_1 \\right\\rangle + \\lambda_2 \\cdot \\left| \\psi_2 \\right\\rangle \\right)} = \\lambda_1 \\cdot \\chi{\\left( \\left| \\psi_1 \\right\\rangle \\right)} + \\lambda_2 \\cdot \\chi{\\left( \\left| \\psi_2 \\right\\rangle \\right)}} $$<\/div><\/dd><\/dl>

\u3053\u308c\u3089\u306e\u7dda\u5f62\u95a2\u6570\u306e\u96c6\u5408\u306f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3092\u69cb\u6210\u3057\u307e\u3059

$$ {\\ \\epsilon^*\\} $$<\/div>\u306e\u4e8c\u91cd\u7a7a\u9593<\/i>\u3068\u547c\u3070\u308c\u308b$$ {\\ \\epsilon\\} $$<\/p><\/div> \u3002\u3053\u306e\u30bb\u30c3\u30c8\u306e\u8981\u7d20\u3092\u30d9\u30af\u30c8\u30eb\u30d6\u30e9<\/strong>\u307e\u305f\u306f\u30d6\u30e9<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002
$$ {\\left\\langle \\phi \\right|} $$<\/div> \u3002

\u3057\u305f\u304c\u3063\u3066\u3001\u7dda\u5f62\u95a2\u6570\u304c

$$ {\\ \\chi\\} $$<\/div>\u306b\u4f5c\u7528\u3059\u308b
$$ {\\left| \\psi \\right\\rangle} $$<\/div> \u3001\u6b21\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <\/p>
$$ {\\chi{\\left( \\left| \\psi \\right\\rangle \\right)} = \\lambda = \\left\\langle \\phi | \\psi \\right\\rangle} $$<\/div><\/dd><\/dl>

\u3053\u306e\u65b0\u3057\u3044\u8868\u8a18\u6cd5\u306f\u3001\u5b9f\u969b\u306b\u3001\u30d6\u30e9\u3001\u30b1\u30c3\u30c8\u3001\u304a\u3088\u3073\u30b1\u30c3\u30c8\u9593\u306e\u30c9\u30c3\u30c8\u7a4d\u306e\u9593\u306b\u5b58\u5728\u3059\u308b\u95a2\u4fc2\u3092\u5f37\u8abf\u3057\u3066\u3044\u307e\u3059\u3002\u30b1\u30c3\u30c8\u3092\u6301\u3063\u3066\u3044\u304d\u307e\u3057\u3087\u3046

$$ {\\left| \\phi \\right\\rangle} $$<\/div> \u3002\u305d\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u306f\u3001
$$ {\\left| \\psi \\right\\rangle} $$<\/div>\u756a\u53f7\u3092\u4e0e\u3048\u308b
$$ {\\ \\lambda\\} $$<\/div> \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u7dda\u5f62\u95a2\u6570\u3092\u5b9a\u7fa9\u3057\u307e\u3057\u305f\u3002
$$ {\\left| \\psi \\right\\rangle} $$<\/div>\u8907\u7d20\u6570\u306b\u4e00\u81f4\u3057\u307e\u3059
$$ {\\ \\lambda\\} $$<\/div> \u3001 \u304b\u3089
$$ {\\left| \\phi \\right\\rangle} $$<\/div> : <\/p>
$$ {\\phi{(|\\psi\\rangle)} = \\lambda = \\left( \\left| \\phi \\right\\rangle, \\left| \\psi \\right\\rangle \\right)} $$<\/div><\/dd><\/dl>

\u3053\u306e\u6a5f\u80fd\u304c\u6ce8\u76ee\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3001

$$ {\\left\\langle \\phi \\right|} $$<\/div> \u3001\u6b21\u306e\u3088\u3046\u306b\u3082\u66f8\u304d\u307e\u3059\u3002 <\/p>
$$ {\\left( \\left| \\phi \\right\\rangle, \\left| \\psi \\right\\rangle \\right) = \\left\\langle \\phi \\right| \\cdot \\left| \\psi \\right\\rangle = \\left\\langle \\phi | \\psi \\right\\rangle} $$<\/div><\/dd><\/dl>

\u3053\u308c\u306b\u3088\u308a\u3001\u5404\u30b1\u30c3\u30c8\u306f\u30b9\u30ab\u30e9\u30fc\u7a4d\u306a\u3069\u306e\u30d6\u30e9\u30b8\u30e3\u30fc\u306b\u5bfe\u5fdc\u3059\u308b\u3068\u8a00\u3048<\/i>\u307e\u3059\u3002

$$ {\\left( \\left| \\phi \\right\\rangle, \\left| \\psi \\right\\rangle \\right)} $$<\/div>\u66f8\u304b\u308c\u3066\u3044\u307e\u3059
$$ {\\left\\langle \\phi | \\psi \\right\\rangle} $$<\/div> \u3002\u3057\u304b\u3057\u3001\u3053\u306e\u5bfe\u5fdc\u306f\u6c7a\u3057\u3066<\/i>\u76f8\u4e92\u7684\u3067<\/a><\/span>\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u300c\u30b1\u30c3\u30c8\u7b49\u4fa1\u7269\u300d\u3092\u6301\u305f\u306a\u3044 (\u975e\u7dda\u5f62) \u30a2\u30fc\u30e0\u304c\u5b58\u5728\u3057\u307e\u3059 (\u3053\u308c\u3089\u306e\u30a2\u30fc\u30e0\u306f\u975e\u7dda\u5f62\u95a2\u6570\u3067\u3042\u308a\u3001\u65b9\u7a0b\u5f0f\u306b ket \u89e3\u304c\u306a\u3044\u304b\u3001\u307e\u305f\u306f ket \u89e3\u304c\u5b58\u5728\u3057\u306a\u3044\u305f\u3081\u3001\u7b49\u4fa1\u6027\u306b\u95a2\u3059\u308b\u4e00\u610f\u306e ket \u304c\u5b58\u5728\u3057\u307e\u305b\u3093)\u3002\u65b9\u7a0b\u5f0f\u306e\u3044\u304f\u3064\u304b\u306e ket \u89e3)\u3002<\/p>

\u66f8\u304d\u8fbc\u307f

$$ {\\left\\langle \\phi | \\psi \\right\\rangle} $$<\/div> 1 \u3064\u306f\u95a2\u6570\u3092\u30b1\u30c3\u30c8\u306b\u9069\u7528\u3057\u305f\u7d50\u679c\u3067\u3042\u308a\u3001\u3082\u3046 1 \u3064\u306f 2 \u3064\u306e\u30b1\u30c3\u30c8\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u3067\u3059\u3002<\/p>

\u30d7\u30ed\u30d1\u30c6\u30a3<\/span><\/h3>
\n\"\u62ec\u5f27\u8868\u8a18\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

bra \u3068 ket \u306e\u9593\u306b\u306f\u5bfe\u5fdc\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>

$$ {\\left| \\psi \\right\\rangle \\rightarrow \\left\\langle \\psi \\right|} $$<\/div> \uff08\u3057\u304b\u3057
$$ {\\left\\langle \\psi \\right| \\rightarrow \\left| \\psi \\right\\rangle} $$<\/div>\u5e38\u306b\u771f\u5b9f\u3067\u3042\u308b\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002)<\/dd><\/dl>

\u30c9\u30c3\u30c8\u7a4d\u306e\u53cd\u7dda\u5f62\u6027\u306f\u3001\u6b21\u306e\u5bfe\u5fdc\u3092\u610f\u5473\u3057\u307e\u3059\u3002 <\/p>

$$ {\\lambda \\cdot \\left| \\psi \\right\\rangle \\rightarrow \\lambda^* \\cdot \\left\\langle \\psi \\right|} $$<\/div><\/dd><\/dl>

\u78ba\u304b\u306b\u3001\u305d\u306e\u57fa\u6e96\u306f\u3001

$$ {\\lambda \\cdot \\left| \\psi \\right\\rangle} $$<\/div>\u306f\u6b63\u5b9a\u5024\u3067\u3059: <\/p>
$$ {{\\left|\\left| \\lambda \\cdot \\left| \\psi \\right\\rangle \\right|\\right|}^2 = \\lambda \\cdot \\lambda^* \\cdot \\left\\langle \\psi | \\psi \\right\\rangle = \\left( \\lambda^* \\cdot \\left\\langle \\psi \\right| \\right) \\cdot \\left( \\lambda \\cdot \\left| \\psi \\right\\rangle \\right)} $$<\/div><\/dd><\/dl>

\u30b1\u30c3\u30c8\u3092\u8b58\u5225\u3057\u307e\u3059

$$ {\\lambda \\cdot \\left| \\psi \\right\\rangle} $$<\/div>\u3053\u308c\u306f\u3001\u5f0f\u306e\u300c\u6b8b\u308a\u300d\u304c\u7dda\u5f62\u95a2\u6570\u306e\u53cc\u5bfe\u7a7a\u9593\u5185\u306e\u5bfe\u5fdc\u3059\u308b\u3082\u306e\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>

\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8<\/span><\/h3>

\u30ce\u30eb\u30e0\u3092\u8a18\u8ff0\u3059\u308b\u3068\u3001\u53cc\u5bfe\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306e\u5f62\u5f0f\u3067\u30d6\u30e9\u30b8\u30e3\u30fc\u3092\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002

$$ {\\ \\epsilon^*\\} $$<\/div>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3068\u540c\u3058\u6b21\u5143
$$ {\\ \\epsilon\\} $$<\/div>\u72b6\u614b: <\/p>
$$ {\\dim{\\left( \\epsilon \\right)} = \\dim{\\left( \\epsilon^* \\right)} = N} $$<\/div> \u3001 <\/dd>
$$ {\\left\\langle \\phi \\right| = \\sum_{n = 1}^N{\\phi_n \\cdot \\left\\langle u_n \\right|}} $$<\/div> \u3001 <\/dd>
$$ {\\left| \\psi \\right\\rangle = \\sum_{n = 1}^N{\\psi_n \\cdot \\left| u_n \\right\\rangle}} $$<\/div> \u3002<\/dd><\/dl>

\u307e\u305f\u3001\u8155\u3092\u3001\u6c34\u5e73\u306b\u914d\u7f6e\u3055\u308c\u305f\u4e00\u9023\u306e\u6570\u5024 (\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8) \u3067\u3042\u308b\u7dda\u30d9\u30af\u30c8\u30eb<\/i>\u306e\u5f62\u5f0f\u3067\u8868\u3057\u307e\u3059\u3002 <\/p>

$$ {\\left\\langle \\phi \\right| = \\begin{pmatrix} \\phi_1 \\\\ \\phi_2 \\\\ \\vdots \\\\ \\phi_N \\end{pmatrix}_{\\epsilon^*} = \\begin{bmatrix} \\phi_1 & \\phi_2 & \\cdots & \\phi_N \\end{bmatrix} \\cdot \\begin{bmatrix} \\left\\langle u_1 \\right| \\\\ \\left\\langle u_2 \\right| \\\\ \\vdots \\\\ \\left\\langle u_N \\right| \\end{bmatrix}} $$<\/div><\/dd><\/dl>

\u884c\u884c\u5217\u306b\u306f\u30b9\u30ab\u30e9\u30fc\u306e\u307f\u304c\u542b\u307e\u308c\u3001\u5217\u884c\u5217\u306b\u306f\u30e6\u30cb\u30c3\u30c8\u30a2\u30fc\u30e0\u306e\u307f\u304c\u542b\u307e\u308c\u3001\u30b9\u30ab\u30e9\u30fc\u3068\u30a2\u30fc\u30e0\u306e\u7a4d\u306f\u53ef\u63db\u3067\u3042\u308b\u305f\u3081\u3001\u4e0a\u8a18\u306e\u884c\u5217\u7a4d<\/a><\/span>\u306f\u53ef\u63db\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u307e\u305f\u3001\u884c\u5217\u7a4d d \u304c\u5217\u884c\u5217\u3068\u884c\u884c\u5217\u306e\u5834\u5408\u3001\u5b9a\u7fa9\u3055\u308c\u3066\u304a\u308a\u3001\u5e38\u306b\u53ef\u63db\u3067\u3059\u3002\u30b9\u30ab\u30e9\u30fc\u306e\u5217\u884c\u5217\u3068\u30b1\u30c3\u30c8\u306e\u884c\u884c\u5217\u306e\u884c\u5217\u7a4d\u3082\u540c\u69d8\u3067\u3059\u3002<\/p>

\u305d\u306e\u5f8c\u3001\u30d6\u30e9\u3068\u30b1\u30c3\u30c8\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u3092\u30014 \u3064\u306e\u884c\u5217 (2 \u3064\u306e\u30b9\u30ab\u30e9\u30fc\u884c\u5217\u3068\u30e6\u30cb\u30c3\u30c8 \u30a2\u30fc\u30e0\u307e\u305f\u306f\u30e6\u30cb\u30c3\u30c8 \u30b1\u30c3\u30c8\u306e\u884c\u5217) \u306e\u7a4d\u306e\u5f62\u5f0f\u3067\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30b9\u30ab\u30e9\u30fc\u884c\u5217\u3092\u4e26\u3079\u66ff\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u30e6\u30cb\u30c3\u30c8 \u30a2\u30fc\u30e0\u884c\u5217\u3068\u30e6\u30cb\u30c3\u30c8 \u30b1\u30c3\u30c8\u306e\u7a4d\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u304c\u6b8b\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u3053\u308c\u3089\u306e\u30e6\u30cb\u30bf\u30ea\u884c\u5217\u304c\u8ee2\u7f6e\u304a\u3088\u3073\u5171\u5f79\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u76ee\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u305d\u308c\u3089\u306e\u7a4d\u304c\u305d\u308c\u3089\u306e\u30ce\u30eb\u30e0\u306e\u7a4d\u306b\u63db\u7b97\u3055\u308c\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u5b9a\u7fa9\u4e0a\u3001\u5358\u4f4d\u884c\u5217\u306e\u30ce\u30eb\u30e0\u306f 1 \u3067\u3042\u308b\u305f\u3081\u3001\u3053\u308c\u3089\u306e\u5358\u4f4d\u884c\u5217\u306f\u5185\u7a4d\u304b\u3089\u524a\u9664\u3067\u304d\u307e\u3059\u3002\u30b9\u30ab\u30e9\u30fc\u7a4d\u306e\u5b9a\u7fa9\u81ea\u4f53\u306b\u3088\u308a\u3001\u6b21\u306e\u3088\u3046\u306b 2 \u3064\u306e\u30b9\u30ab\u30e9\u30fc\u884c\u5217\u306e\u7a4d\u3068\u3044\u3046\u89b3\u70b9\u304b\u3089\u7c21\u5358\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {\\left\\langle \\phi | \\psi \\right\\rangle = \\left( \\begin{pmatrix} \\phi_1 \\\\ \\phi_2 \\\\ \\vdots \\\\ \\phi_N \\end{pmatrix}_{\\epsilon^*}, \\begin{pmatrix} \\psi_1 \\\\ \\psi_2 \\\\ \\vdots \\\\ \\psi_N \\end{pmatrix}_{\\epsilon} \\right) = \\begin{bmatrix} \\phi_1 & \\phi_2 & \\cdots & \\phi_N \\end{bmatrix} \\cdot \\begin{bmatrix} \\psi_1 \\\\ \\psi_2 \\\\ \\vdots \\\\ \\psi_N \\end{bmatrix} = \\sum_{n = 1}^N{\\phi_n \\cdot \\psi_n}} $$<\/div><\/dd><\/dl>

\u8a9e\u6e90<\/span><\/h2>

\u82f1\u8a9e\u3067\u30d6\u30e9\u30b1\u30c3\u30c8\u306f\u300c\u30d5\u30c3\u30af\u300d\u3092\u610f\u5473\u3057\u3001\u3053\u308c\u304c\u30d6\u30e9\u30b1\u30c3\u30c8\u306e\u540d\u524d\u306e\u7531\u6765\u3068\u306a\u308a\u3001\u300c\u5de6\u8237\u300d\u3068\u300c\u53f3\u8237\u300d\u306b\u5c11\u3057\u4f3c\u3066\u3044\u307e\u3059\u3002<\/p>

\u30c7\u30a3\u30e9\u30c3\u30af\u6f14\u7b97\u5b50\u3068\u8868\u8a18\u6cd5<\/span><\/h2>

\u4e00\u822c\u306b\u3001\u7a7a\u9593\u306b\u4f5c\u7528\u3059\u308b\u7dda\u5f62\u6f14\u7b97\u5b50\u306f\u3001

$$ {\\ \\epsilon\\} $$<\/div>\u72b6\u614b\u306f\u3001\u6b21\u306e\u5f62\u5f0f\u306e\u6f14\u7b97\u5b50\u306e\u7dda\u5f62\u7d50\u5408\u306e\u5f62\u5f0f\u3067\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>
$$ {\\left| \\psi \\right\\rangle \\cdot \\left\\langle \\varphi \\right|} $$<\/div> \u3001<\/dd><\/dl>

\u72b6\u614b\u306b\u5bfe\u3059\u308b\u30a2\u30af\u30b7\u30e7\u30f3\u306f ket \u3067\u8868\u3055\u308c\u307e\u3059

$$ {\\left| \\phi \\right\\rangle} $$<\/div> \u3001\u5358\u306b\u72b6\u614b\u306b\u306a\u308a\u307e\u3059: <\/p>
$$ {\\left\\langle \\varphi | \\phi \\right\\rangle \\cdot \\left| \\psi \\right\\rangle} $$<\/div> \u3001<\/dd><\/dl>

\u66f8\u9762\u3067\u306e\u5927\u5e45\u306a\u7bc0\u7d04\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002<\/p><\/div>\n

\u53c2\u8003\u8cc7\u6599<\/h2>\n
  1. \u0631\u0645\u0632 \u0628\u0631\u0627\u0643\u064a\u062a \u2013 arabe<\/a><\/li>
  2. \u0411\u0440\u0430 \u0456 \u043a\u0435\u0442 \u2013 bi\u00e9lorusse<\/a><\/li>
  3. \u09ac\u09cd\u09b0\u09be-\u0995\u09c7\u099f \u09aa\u09cd\u09b0\u09a4\u09bf\u0995 \u2013 bengali<\/a><\/li>
  4. Bra\u2013ket notacija \u2013 bosniaque<\/a><\/li>
  5. Notaci\u00f3 bra-ket \u2013 catalan<\/a><\/li>
  6. Diracova notace \u2013 tch\u00e8que<\/a><\/li><\/ol>\n
    \n

    \n \u62ec\u5f27\u8868\u8a18\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n