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Display information for equation id:math.1762.25 on revision:1762

* Page found: Homöopolare chemische Bindung des Wasserstoffmoleküls (eq math.1762.25)

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Homöopolare chemische Bindung des Wasserstoffmoleküls Eq: math.1762.25

Hash: ba3ceef49506d4d723846f82e0de7f2f

TeX (original user input):

\begin{align}
& {{{\hat{H}}}^{(1)}}_{\alpha ,\alpha }=\left\langle  {{\Psi }_{\alpha }} \right|{{{\hat{H}}}^{(1)}}\left| {{\Psi }_{\alpha }} \right\rangle {{=}_{1}}{{\left\langle  a \right|}_{2}}\left\langle  b \right|{{{\hat{H}}}^{(1)}}{{\left| b \right\rangle }_{2}}{{\left| a \right\rangle }_{1}} \\
& \Rightarrow {{{\hat{H}}}^{(1)}}_{\alpha ,\alpha }=\int_{{}}^{{}}{{{d}^{3}}{{r}_{1}}\int_{{}}^{{}}{{}}{{d}^{3}}{{r}_{2}}{{\left| {{\Psi }_{a}}({{{\bar{r}}}_{1}}) \right|}^{2}}{{\left| {{\Psi }_{b}}({{{\bar{r}}}_{2}}) \right|}^{2}}{{{\hat{H}}}^{(1)}}=}{{{\hat{H}}}^{(1)}}_{\beta \beta } \\
\end{align}

TeX (checked):

{\begin{aligned}&{{\hat {H}}^{(1)}}_{\alpha ,\alpha }=\left\langle {{\Psi }_{\alpha }}\right|{{\hat {H}}^{(1)}}\left|{{\Psi }_{\alpha }}\right\rangle {{=}_{1}}{{\left\langle a\right|}_{2}}\left\langle b\right|{{\hat {H}}^{(1)}}{{\left|b\right\rangle }_{2}}{{\left|a\right\rangle }_{1}}\\&\Rightarrow {{\hat {H}}^{(1)}}_{\alpha ,\alpha }=\int _{}^{}{{{d}^{3}}{{r}_{1}}\int _{}^{}{}{{d}^{3}}{{r}_{2}}{{\left|{{\Psi }_{a}}({{\bar {r}}_{1}})\right|}^{2}}{{\left|{{\Psi }_{b}}({{\bar {r}}_{2}})\right|}^{2}}{{\hat {H}}^{(1)}}=}{{\hat {H}}^{(1)}}_{\beta \beta }\\\end{aligned}}

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\begin{aligned} {\hat{H}}^{(1)}_{α, α} = ⟨ Ψ_{α} | {\hat{H}}^{(1)} | Ψ_{α} ⟩ =_{1} {⟨ a |}_{2} ⟨ b | {\hat{H}}^{(1)} {| b ⟩}_{2} {| a ⟩}_{1} \\ \Rightarrow {\hat{H}}^{(1)}_{α, α} = \int_{}^{} d^{3} r_{1} \int_{}^{} d^{3} r_{2} {| Ψ_{a} ({\bar{r}}_{1}) |}^{2} {| Ψ_{b} ({\bar{r}}_{2}) |}^{2} {\hat{H}}^{(1)} = {\hat{H}}^{(1)}_{β β} \end{aligned}

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Identifiers

${\hat{H}}_{α, α}$

$Ψ_{α}$

$\hat{H}$

$Ψ_{α}$

$a_{2}$

$b$

$\hat{H}$

$b_{2}$

$a_{1}$

${\hat{H}}_{α, α}$

$r_{1}$

$r_{2}$

$Ψ_{a}$

${\bar{r}}_{1}$

$Ψ_{b}$

${\bar{r}}_{2}$

$\hat{H}$

${\hat{H}}_{β β}$

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