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Display information for equation id:math.1758.28 on revision:1758
* Page found: Homöopolare chemische Bindung des Wasserstoffmoleküls (eq math.1758.28)
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Hash: 04fbf751974a535caa1d359d211c1fad
TeX (original user input):
\begin{align}
& {{{\hat{H}}}^{(1)}}_{\alpha \beta }=\left\langle {{\Psi }_{\alpha }} \right|{{{\hat{H}}}^{(1)}}\left| {{\Psi }_{\beta }} \right\rangle {{=}_{1}}{{\left\langle a \right|}_{2}}\left\langle b \right|{{{\hat{H}}}^{(1)}}{{\left| a \right\rangle }_{2}}{{\left| b \right\rangle }_{1}} \\
& \Rightarrow {{{\hat{H}}}^{(1)}}_{\alpha \beta }=\int_{{}}^{{}}{{{d}^{3}}{{r}_{1}}\int_{{}}^{{}}{{}}{{d}^{3}}{{r}_{2}}{{\Psi }_{a}}{{({{{\bar{r}}}_{1}})}^{*}}{{\Psi }_{b}}({{{\bar{r}}}_{1}}){{\Psi }_{b}}{{({{{\bar{r}}}_{2}})}^{*}}{{\Psi }_{a}}({{{\bar{r}}}_{2}}){{{\hat{H}}}^{(1)}}=}{{{\hat{H}}}^{(1)}}_{\beta \alpha }=:A \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\hat {H}}^{(1)}}_{\alpha \beta }=\left\langle {{\Psi }_{\alpha }}\right|{{\hat {H}}^{(1)}}\left|{{\Psi }_{\beta }}\right\rangle {{=}_{1}}{{\left\langle a\right|}_{2}}\left\langle b\right|{{\hat {H}}^{(1)}}{{\left|a\right\rangle }_{2}}{{\left|b\right\rangle }_{1}}\\&\Rightarrow {{\hat {H}}^{(1)}}_{\alpha \beta }=\int _{}^{}{{{d}^{3}}{{r}_{1}}\int _{}^{}{}{{d}^{3}}{{r}_{2}}{{\Psi }_{a}}{{({{\bar {r}}_{1}})}^{*}}{{\Psi }_{b}}({{\bar {r}}_{1}}){{\Psi }_{b}}{{({{\bar {r}}_{2}})}^{*}}{{\Psi }_{a}}({{\bar {r}}_{2}}){{\hat {H}}^{(1)}}=}{{\hat {H}}^{(1)}}_{\beta \alpha }=:A\\\end{aligned}}
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data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>a</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><msub><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>α</mi><mi>β</mi></mrow></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mo>*</mo></mrow></msup><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>b</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>b</mi></mrow></msub><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mo>*</mo></mrow></msup><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mo>=</mo></mrow><msub><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>β</mi><mi>α</mi></mrow></mrow></msub><mo>=</mo><mi>:</mi><mi>A</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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