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Display information for equation id:math.2564.29 on revision:2564
* Page found: Das Photonengas im Strahlungshohlraum (eq math.2564.29)
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Hash: 5ad2d3568ff583d696d2cc5efd504bef
TeX (original user input):
\begin{align}
& \frac{\left\langle {{N}_{2}} \right\rangle }{\left\langle {{N}_{1}} \right\rangle }=\frac{{{g}_{2}}P({{E}_{2}})}{{{g}_{1}}P({{E}_{1}})}=\frac{{{g}_{2}}{{e}^{-\beta {{E}_{2}}}}}{{{g}_{1}}{{e}^{-\beta {{E}_{1}}}}}=\frac{{{g}_{2}}}{{{g}_{1}}}{{e}^{-\beta \left( {{E}_{2}}-{{E}_{1}} \right)}}=\frac{{{g}_{2}}}{{{g}_{1}}}{{e}^{-\beta h\nu }} \\
& h\nu ={{E}_{2}}-{{E}_{1}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{\frac {\left\langle {{N}_{2}}\right\rangle }{\left\langle {{N}_{1}}\right\rangle }}={\frac {{{g}_{2}}P({{E}_{2}})}{{{g}_{1}}P({{E}_{1}})}}={\frac {{{g}_{2}}{{e}^{-\beta {{E}_{2}}}}}{{{g}_{1}}{{e}^{-\beta {{E}_{1}}}}}}={\frac {{g}_{2}}{{g}_{1}}}{{e}^{-\beta \left({{E}_{2}}-{{E}_{1}}\right)}}={\frac {{g}_{2}}{{g}_{1}}}{{e}^{-\beta h\nu }}\\&h\nu ={{E}_{2}}-{{E}_{1}}\\\end{aligned}}
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MathML (3.59 KB / 482 B) :
<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><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mi>P</mi><mo stretchy="false">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>P</mi><mo stretchy="false">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>β</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>β</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></msup></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>β</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>β</mi><mi>h</mi><mi>ν</mi></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mi>h</mi><mi>ν</mi><mo>=</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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