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* Page found: Identische Teilchen: Spin und Statistik (eq math.1720.87)

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Identische Teilchen: Spin und Statistik Eq: math.1720.87

Hash: 59da5960c2bbe2c5fc67ce4513f59b21

TeX (original user input):

\begin{align}
& {{\left| {{\Psi }_{ab}}\left( \bar{r},\bar{r} \right) \right|}^{2}}={{\left| \left\langle  \bar{r}\bar{r} \right|{{\left| ab \right\rangle }_{a}} \right|}^{2}}=\frac{1}{2}{{\left| _{1}\left\langle  {\bar{r}} \right|{{\left| a \right\rangle }_{1}}_{2}\left\langle  {\bar{r}} \right|{{\left| b \right\rangle }_{2}}{{-}_{1}}\left\langle  _{1} \right|{{\left| a \right\rangle }_{1}}_{2}\left\langle  {\bar{r}} \right|{{\left| b \right\rangle }_{2}} \right|}^{2}} \\
& =\frac{1}{2}{{\left| {{\Psi }_{a}}\left( {\bar{r}} \right){{\Psi }_{b}}\left( {\bar{r}} \right)-{{\Psi }_{b}}\left( {\bar{r}} \right){{\Psi }_{a}}\left( {\bar{r}} \right) \right|}^{2}}=0 \\
\end{align}

TeX (checked):

{\begin{aligned}&{{\left|{{\Psi }_{ab}}\left({\bar {r}},{\bar {r}}\right)\right|}^{2}}={{\left|\left\langle {\bar {r}}{\bar {r}}\right|{{\left|ab\right\rangle }_{a}}\right|}^{2}}={\frac {1}{2}}{{\left|_{1}\left\langle {\bar {r}}\right|{{\left|a\right\rangle }_{1}}_{2}\left\langle {\bar {r}}\right|{{\left|b\right\rangle }_{2}}{{-}_{1}}\left\langle _{1}\right|{{\left|a\right\rangle }_{1}}_{2}\left\langle {\bar {r}}\right|{{\left|b\right\rangle }_{2}}\right|}^{2}}\\&={\frac {1}{2}}{{\left|{{\Psi }_{a}}\left({\bar {r}}\right){{\Psi }_{b}}\left({\bar {r}}\right)-{{\Psi }_{b}}\left({\bar {r}}\right){{\Psi }_{a}}\left({\bar {r}}\right)\right|}^{2}}=0\\\end{aligned}}

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\begin{aligned} {| Ψ_{a b} (\bar{r}, \bar{r}) |}^{2} = {| ⟨ \bar{r} \bar{r} | {| a b ⟩}_{a} |}^{2} = \frac{1}{2} {| 1 ⟨ \bar{r} | {| a ⟩}_{1}_{2} ⟨ \bar{r} | {| b ⟩}_{2} -_{1} ⟨ 1 | {| a ⟩}_{1}_{2} ⟨ \bar{r} | {| b ⟩}_{2} |}^{2} \\ = \frac{1}{2} {| Ψ_{a} (\bar{r}) Ψ_{b} (\bar{r}) - Ψ_{b} (\bar{r}) Ψ_{a} (\bar{r}) |}^{2} = 0 \end{aligned}

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Identifiers

$Ψ_{a b}$

$\bar{r}$

$\bar{r}$

$\bar{r}$

$\bar{r}$

$a$

$b$

$a$

$\bar{r}$

$a_{1} 2$

$\bar{r}$

$b_{2}$

$a_{1} 2$

$\bar{r}$

$b_{2}$

$Ψ_{a}$

$\bar{r}$

$Ψ_{b}$

$\bar{r}$

$Ψ_{b}$

$\bar{r}$

$Ψ_{a}$

$\bar{r}$

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