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Display information for equation id:math.1734.14 on revision:1734
* Page found: Induzierte Emission und Absorption von Lichtquanten in Atomen (eq math.1734.14)
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Hash: 26063462d823bd17014645b7ddc05af6
TeX (original user input):
\begin{align}
& \bar{E}(\bar{r},t)=\int_{0}^{\infty }{d\omega }{{{\bar{E}}}_{0}}(\omega )\sin \left( \bar{k}\bar{r}-\omega t \right) \\
& \Rightarrow {{W}_{nn0}}=\frac{\pi }{2{{\hbar }^{2}}}\int_{0}^{\infty }{d\left( \hbar \omega \right)}{{\left( {{{\bar{E}}}_{0}}\left( \omega \right)\cdot {{{\bar{d}}}_{nn0}} \right)}^{2}}\left\{ \delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega ) \right\} \\
\end{align}
TeX (checked):
{\begin{aligned}&{\bar {E}}({\bar {r}},t)=\int _{0}^{\infty }{d\omega }{{\bar {E}}_{0}}(\omega )\sin \left({\bar {k}}{\bar {r}}-\omega t\right)\\&\Rightarrow {{W}_{nn0}}={\frac {\pi }{2{{\hbar }^{2}}}}\int _{0}^{\infty }{d\left(\hbar \omega \right)}{{\left({{\bar {E}}_{0}}\left(\omega \right)\cdot {{\bar {d}}_{nn0}}\right)}^{2}}\left\{\delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega )\right\}\\\end{aligned}}
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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mover><mi>E</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ω</mi></mrow><msub><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mi>sin</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>k</mi><mo>¯</mo></mover><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mi>ω</mi><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><msub><mi>W</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>π</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msup><mi alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>d</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi alternate="1">ℏ</mi><mi>ω</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">⋅</mo><msub><mover><mi>d</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mi>δ</mi><mo stretchy="false">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo stretchy="false">−</mo><mi alternate="1">ℏ</mi><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">+</mo><mi>δ</mi><mo stretchy="false">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo stretchy="false">+</mo><mi alternate="1">ℏ</mi><mi>ω</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">}</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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