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Display information for equation id:math.1681.8 on revision:1681
* Page found: Das Wasserstoffatom (eq math.1681.8)
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TeX (original user input):
\begin{align}
& -\frac{{{\hbar }^{2}}}{2{{m}_{1}}}{{\Delta }_{1}}-\frac{{{\hbar }^{2}}}{2{{m}_{2}}}{{\Delta }_{2}}=-\frac{{{\hbar }^{2}}}{2}\left\{ \frac{{{m}_{1}}}{{{M}^{2}}}{{\Delta }_{R}}+\frac{2}{M}{{\nabla }_{R}}{{\nabla }_{r}}+\frac{1}{{{m}_{1}}}{{\Delta }_{r}}+\frac{{{m}_{2}}}{{{M}^{2}}}{{\Delta }_{R}}-\frac{2}{M}{{\nabla }_{R}}{{\nabla }_{r}}+\frac{1}{{{m}_{2}}}{{\Delta }_{r}} \right\} \\
& -\frac{{{\hbar }^{2}}}{2{{m}_{1}}}{{\Delta }_{1}}-\frac{{{\hbar }^{2}}}{2{{m}_{2}}}{{\Delta }_{2}}=-\frac{{{\hbar }^{2}}}{2M}{{\Delta }_{R}}-\frac{{{\hbar }^{2}}}{2m}{{\Delta }_{r}} \\
\end{align}
TeX (checked):
{\begin{aligned}&-{\frac {{\hbar }^{2}}{2{{m}_{1}}}}{{\Delta }_{1}}-{\frac {{\hbar }^{2}}{2{{m}_{2}}}}{{\Delta }_{2}}=-{\frac {{\hbar }^{2}}{2}}\left\{{\frac {{m}_{1}}{{M}^{2}}}{{\Delta }_{R}}+{\frac {2}{M}}{{\nabla }_{R}}{{\nabla }_{r}}+{\frac {1}{{m}_{1}}}{{\Delta }_{r}}+{\frac {{m}_{2}}{{M}^{2}}}{{\Delta }_{R}}-{\frac {2}{M}}{{\nabla }_{R}}{{\nabla }_{r}}+{\frac {1}{{m}_{2}}}{{\Delta }_{r}}\right\}\\&-{\frac {{\hbar }^{2}}{2{{m}_{1}}}}{{\Delta }_{1}}-{\frac {{\hbar }^{2}}{2{{m}_{2}}}}{{\Delta }_{2}}=-{\frac {{\hbar }^{2}}{2M}}{{\Delta }_{R}}-{\frac {{\hbar }^{2}}{2m}}{{\Delta }_{r}}\\\end{aligned}}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mi>M</mi></mrow></mfrac></mrow><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mi>M</mi></mrow></mfrac></mrow><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo data-mjx-texclass="CLOSE">}</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>M</mi></mrow></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><msub><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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