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Display information for equation id:math.1720.77 on revision:1720

* Page found: Identische Teilchen: Spin und Statistik (eq math.1720.77)

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\begin{align}
& {{f}_{n}}{{^{2}}_{a}}\left\langle  {{a}_{1}},...,{{a}_{N}} \right|{{\left| {{a}_{1}},...,{{a}_{N}} \right\rangle }_{a}}={{f}_{n}}^{2}\left( _{1}\left\langle  {{a}_{1}} \right|{{...}_{N}}\left\langle  {{a}_{N}} \right| \right)\hat{A}\hat{A}\left( {{\left| {{a}_{1}} \right\rangle }_{1}}...{{\left| {{a}_{N}} \right\rangle }_{N}} \right) \\
& ={{f}_{n}}^{2}\left( _{1}\left\langle  {{a}_{1}} \right|{{...}_{N}}\left\langle  {{a}_{N}} \right| \right)\hat{A}\left( {{\left| {{a}_{1}} \right\rangle }_{1}}...{{\left| {{a}_{N}} \right\rangle }_{N}} \right)={{f}_{n}}^{2}\left( _{1}\left\langle  {{a}_{1}} \right|{{...}_{N}}\left\langle  {{a}_{N}} \right| \right)\frac{1}{N!}\left| \begin{matrix}
{{\left| {{a}_{1}} \right\rangle }_{1}} & {{\left| {{a}_{1}} \right\rangle }_{2}} & ... & {{\left| {{a}_{1}} \right\rangle }_{N}}  \\
{{\left| {{a}_{2}} \right\rangle }_{1}} & {{\left| {{a}_{2}} \right\rangle }_{2}} & ... & {{\left| {{a}_{2}} \right\rangle }_{N}}  \\.
.. & ... & ... & ...  \\
{{\left| {{a}_{N}} \right\rangle }_{1}} & {{\left| {{a}_{N}} \right\rangle }_{2}} & ... & {{\left| {{a}_{N}} \right\rangle }_{N}}  \\
\end{matrix} \right| \\
& ={{f}_{n}}^{2}\frac{1}{N!}\left| \begin{matrix}
_{1}\left\langle  {{a}_{1}} \right|{{\left| {{a}_{1}} \right\rangle }_{1}} & _{2}\left\langle  {{a}_{2}} \right|{{\left| {{a}_{1}} \right\rangle }_{2}} & ... & _{N}\left\langle  {{a}_{N}} \right|{{\left| {{a}_{1}} \right\rangle }_{N}}  \\
_{1}\left\langle  {{a}_{1}} \right|{{\left| {{a}_{2}} \right\rangle }_{1}} & _{2}\left\langle  {{a}_{2}} \right|{{\left| {{a}_{2}} \right\rangle }_{2}} & ... & _{N}\left\langle  {{a}_{N}} \right|{{\left| {{a}_{2}} \right\rangle }_{N}}  \\.
.. & ... & ... & ...  \\
_{1}\left\langle  {{a}_{1}} \right|{{\left| {{a}_{N}} \right\rangle }_{1}} & _{2}\left\langle  {{a}_{2}} \right|{{\left| {{a}_{N}} \right\rangle }_{2}} & ... & _{N}\left\langle  {{a}_{N}} \right|{{\left| {{a}_{N}} \right\rangle }_{N}}  \\
\end{matrix} \right| \\
& _{1}\left\langle  {{a}_{1}} \right|{{\left| {{a}_{1}} \right\rangle }_{1}}=1 \\
& _{1}\left\langle  {{a}_{i}} \right|{{\left| {{a}_{j}} \right\rangle }_{1}}=0\quad i\ne j \\
& \Rightarrow {{f}_{n}}^{2}\frac{1}{N!}\left| \begin{matrix}
_{1}\left\langle  {{a}_{1}} \right|{{\left| {{a}_{1}} \right\rangle }_{1}} & _{2}\left\langle  {{a}_{2}} \right|{{\left| {{a}_{1}} \right\rangle }_{2}} & ... & _{N}\left\langle  {{a}_{N}} \right|{{\left| {{a}_{1}} \right\rangle }_{N}}  \\
_{1}\left\langle  {{a}_{1}} \right|{{\left| {{a}_{2}} \right\rangle }_{1}} & _{2}\left\langle  {{a}_{2}} \right|{{\left| {{a}_{2}} \right\rangle }_{2}} & ... & _{N}\left\langle  {{a}_{N}} \right|{{\left| {{a}_{2}} \right\rangle }_{N}}  \\.
.. & ... & ... & ...  \\
_{1}\left\langle  {{a}_{1}} \right|{{\left| {{a}_{N}} \right\rangle }_{1}} & _{2}\left\langle  {{a}_{2}} \right|{{\left| {{a}_{N}} \right\rangle }_{2}} & ... & _{N}\left\langle  {{a}_{N}} \right|{{\left| {{a}_{N}} \right\rangle }_{N}}  \\
\end{matrix} \right|={{f}_{n}}^{2}\frac{1}{N!}\left| \begin{matrix}
1 & 0 & ... & 0  \\
0 & 1 & ... & 0  \\.
.. & ... & ... & ...  \\
0 & 0 & ... & 1  \\
\end{matrix} \right|={{f}_{n}}^{2}\frac{1}{N!}\equiv 1! \\
& \Rightarrow {{f}_{n}}=\sqrt{N!} \\
\end{align}

TeX (checked): 

{\begin{aligned}&{{f}_{n}}{{^{2}}_{a}}\left\langle {{a}_{1}},...,{{a}_{N}}\right|{{\left|{{a}_{1}},...,{{a}_{N}}\right\rangle }_{a}}={{f}_{n}}^{2}\left(_{1}\left\langle {{a}_{1}}\right|{{...}_{N}}\left\langle {{a}_{N}}\right|\right){\hat {A}}{\hat {A}}\left({{\left|{{a}_{1}}\right\rangle }_{1}}...{{\left|{{a}_{N}}\right\rangle }_{N}}\right)\\&={{f}_{n}}^{2}\left(_{1}\left\langle {{a}_{1}}\right|{{...}_{N}}\left\langle {{a}_{N}}\right|\right){\hat {A}}\left({{\left|{{a}_{1}}\right\rangle }_{1}}...{{\left|{{a}_{N}}\right\rangle }_{N}}\right)={{f}_{n}}^{2}\left(_{1}\left\langle {{a}_{1}}\right|{{...}_{N}}\left\langle {{a}_{N}}\right|\right){\frac {1}{N!}}\left|{\begin{matrix}{{\left|{{a}_{1}}\right\rangle }_{1}}&{{\left|{{a}_{1}}\right\rangle }_{2}}&...&{{\left|{{a}_{1}}\right\rangle }_{N}}\\{{\left|{{a}_{2}}\right\rangle }_{1}}&{{\left|{{a}_{2}}\right\rangle }_{2}}&...&{{\left|{{a}_{2}}\right\rangle }_{N}}\\...&...&...&...\\{{\left|{{a}_{N}}\right\rangle }_{1}}&{{\left|{{a}_{N}}\right\rangle }_{2}}&...&{{\left|{{a}_{N}}\right\rangle }_{N}}\\\end{matrix}}\right|\\&={{f}_{n}}^{2}{\frac {1}{N!}}\left|{\begin{matrix}_{1}\left\langle {{a}_{1}}\right|{{\left|{{a}_{1}}\right\rangle }_{1}}&_{2}\left\langle {{a}_{2}}\right|{{\left|{{a}_{1}}\right\rangle }_{2}}&...&_{N}\left\langle {{a}_{N}}\right|{{\left|{{a}_{1}}\right\rangle }_{N}}\\_{1}\left\langle {{a}_{1}}\right|{{\left|{{a}_{2}}\right\rangle }_{1}}&_{2}\left\langle {{a}_{2}}\right|{{\left|{{a}_{2}}\right\rangle }_{2}}&...&_{N}\left\langle {{a}_{N}}\right|{{\left|{{a}_{2}}\right\rangle }_{N}}\\...&...&...&...\\_{1}\left\langle {{a}_{1}}\right|{{\left|{{a}_{N}}\right\rangle }_{1}}&_{2}\left\langle {{a}_{2}}\right|{{\left|{{a}_{N}}\right\rangle }_{2}}&...&_{N}\left\langle {{a}_{N}}\right|{{\left|{{a}_{N}}\right\rangle }_{N}}\\\end{matrix}}\right|\\&_{1}\left\langle {{a}_{1}}\right|{{\left|{{a}_{1}}\right\rangle }_{1}}=1\\&_{1}\left\langle {{a}_{i}}\right|{{\left|{{a}_{j}}\right\rangle }_{1}}=0\quad i\neq j\\&\Rightarrow {{f}_{n}}^{2}{\frac {1}{N!}}\left|{\begin{matrix}_{1}\left\langle {{a}_{1}}\right|{{\left|{{a}_{1}}\right\rangle }_{1}}&_{2}\left\langle {{a}_{2}}\right|{{\left|{{a}_{1}}\right\rangle }_{2}}&...&_{N}\left\langle {{a}_{N}}\right|{{\left|{{a}_{1}}\right\rangle }_{N}}\\_{1}\left\langle {{a}_{1}}\right|{{\left|{{a}_{2}}\right\rangle }_{1}}&_{2}\left\langle {{a}_{2}}\right|{{\left|{{a}_{2}}\right\rangle }_{2}}&...&_{N}\left\langle {{a}_{N}}\right|{{\left|{{a}_{2}}\right\rangle }_{N}}\\...&...&...&...\\_{1}\left\langle {{a}_{1}}\right|{{\left|{{a}_{N}}\right\rangle }_{1}}&_{2}\left\langle {{a}_{2}}\right|{{\left|{{a}_{N}}\right\rangle }_{2}}&...&_{N}\left\langle {{a}_{N}}\right|{{\left|{{a}_{N}}\right\rangle }_{N}}\\\end{matrix}}\right|={{f}_{n}}^{2}{\frac {1}{N!}}\left|{\begin{matrix}1&0&...&0\\0&1&...&0\\...&...&...&...\\0&0&...&1\\\end{matrix}}\right|={{f}_{n}}^{2}{\frac {1}{N!}}\equiv 1!\\&\Rightarrow {{f}_{n}}={\sqrt {N!}}\\\end{aligned}}

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fn2a⟨a1,...,aN||a1,...,aN⟩a=fn2(1⟨a1|...N⟨aN|)A^A^(|a1⟩1...|aN⟩N)=fn2(1⟨a1|...N⟨aN|)A^(|a1⟩1...|aN⟩N)=fn2(1⟨a1|...N⟨aN|)1N!||a1⟩1|a1⟩2...|a1⟩N|a2⟩1|a2⟩2...|a2⟩N............|aN⟩1|aN⟩2...|aN⟩N|=fn21N!|1⟨a1||a1⟩12⟨a2||a1⟩2...N⟨aN||a1⟩N1⟨a1||a2⟩12⟨a2||a2⟩2...N⟨aN||a2⟩N............1⟨a1||aN⟩12⟨a2||aN⟩2...N⟨aN||aN⟩N|1⟨a1||a1⟩1=11⟨ai||aj⟩1=0i≠j⇒fn21N!|1⟨a1||a1⟩12⟨a2||a1⟩2...N⟨aN||a1⟩N1⟨a1||a2⟩12⟨a2||a2⟩2...N⟨aN||a2⟩N............1⟨a1||aN⟩12⟨a2||aN⟩2...N⟨aN||aN⟩N|=fn21N!|10...001...0............00...1|=fn21N!≡1!⇒fn=N!
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data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub></mtd></mtr><mtr><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd></mtr><mtr><mtd><msub><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mspace width="1em"></mspace><mi>i</mi><mo>&#x2260;</mo><mi>j</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><msup><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>!</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><msub><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub></mtd></mtr><mtr><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd></mtr><mtr><mtd><msub><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo>=</mo><msup><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>!</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo>=</mo><msup><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>!</mi></mrow></mrow></mfrac></mrow><mo>&#x2261;</mo><mn>1</mn><mi>!</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>!</mi></mrow></msqrt></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Identische Teilchen: Spin und Statistik page

Identifiers

  • fn
  • a
  • a1
  • aN
  • a1
  • aN
  • a
  • fn
  • a1
  • N
  • aN
  • A^
  • A^
  • a11
  • aNN
  • fn
  • a1
  • N
  • aN
  • A^
  • a11
  • aNN
  • fn
  • a1
  • N
  • aN
  • N
  • a11
  • a12
  • a1N
  • a21
  • a22
  • a2N
  • aN1
  • aN2
  • aNN
  • fn
  • N
  • a1
  • a11
  • a2
  • a12
  • N
  • aN
  • a1N
  • a1
  • a21
  • a2
  • a22
  • N
  • aN
  • a2N
  • a1
  • aN1
  • a2
  • aN2
  • N
  • aN
  • aNN
  • a1
  • a11
  • ai
  • aj1
  • i
  • j
  • fn
  • N
  • a1
  • a11
  • a2
  • a12
  • N
  • aN
  • a1N
  • a1
  • a21
  • a2
  • a22
  • N
  • aN
  • a2N
  • a1
  • aN1
  • a2
  • aN2
  • N
  • aN
  • aNN
  • fn
  • N
  • fn
  • N
  • fn
  • N

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“