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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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22m1Δ122m2Δ2=22{m1M2ΔR+2MRr+1m1Δr+m2M2ΔR2MRr+1m2Δr}22m1Δ122m2Δ2=22MΔR22mΔr
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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">&#x0394;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>=</mo><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">&#x210F;</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">&#x0394;</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">&#x2207;</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><msub><mi mathvariant="normal">&#x2207;</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">&#x0394;</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">&#x0394;</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><mo>&#x2212;</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">&#x2207;</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><msub><mi mathvariant="normal">&#x2207;</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">&#x0394;</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>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">&#x210F;</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">&#x0394;</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">&#x210F;</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">&#x0394;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>=</mo><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">&#x210F;</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">&#x0394;</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi data-mjx-alternate="1">&#x210F;</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">&#x0394;</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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Calculated based on the variables occurring on the entire Das Wasserstoffatom page

Identifiers

  • m1
  • Δ1
  • m2
  • Δ2
  • m1
  • M
  • ΔR
  • M
  • R
  • r
  • m1
  • Δr
  • m2
  • M
  • ΔR
  • M
  • R
  • r
  • m2
  • Δr
  • m1
  • Δ1
  • m2
  • Δ2
  • M
  • ΔR
  • m
  • Δr

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