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Display information for equation id:math.2156.21 on revision:2156
* Page found: Mikroskopisches Modell der Polarisierbarkeit (eq math.2156.21)
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Hash: 3bc4256cf5327ede89a33535cee5f488
TeX (original user input):
\begin{align}
& \bar{p}=Ze\bar{r}=\frac{Z{{e}^{2}}}{{{\omega }_{0}}^{2}{{m}_{e}}}{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{k}},t \right)={{\varepsilon }_{0}}\alpha {{{\bar{E}}}_{a}} \\
& \alpha :=\frac{Z{{e}^{2}}}{{{\omega }_{0}}^{2}{{\varepsilon }_{0}}{{m}_{e}}} \\
& \frac{Z{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{m}_{e}}{{R}^{3}}}:={{\omega }_{0}}^{2} \\
& \Rightarrow \alpha :=\frac{Z{{e}^{2}}}{{{\omega }_{0}}^{2}{{\varepsilon }_{0}}{{m}_{e}}}=4\pi {{R}^{3}}=3{{V}_{Atom}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{\bar {p}}=Ze{\bar {r}}={\frac {Z{{e}^{2}}}{{{\omega }_{0}}^{2}{{m}_{e}}}}{{\bar {E}}_{a}}\left({{\bar {r}}_{k}},t\right)={{\varepsilon }_{0}}\alpha {{\bar {E}}_{a}}\\&\alpha :={\frac {Z{{e}^{2}}}{{{\omega }_{0}}^{2}{{\varepsilon }_{0}}{{m}_{e}}}}\\&{\frac {Z{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{m}_{e}}{{R}^{3}}}}:={{\omega }_{0}}^{2}\\&\Rightarrow \alpha :={\frac {Z{{e}^{2}}}{{{\omega }_{0}}^{2}{{\varepsilon }_{0}}{{m}_{e}}}}=4\pi {{R}^{3}}=3{{V}_{Atom}}\\\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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><mi>Z</mi><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>Z</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub></mrow></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</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"><mi>k</mi></mrow></msub><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>α</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>E</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mi>α</mi><mi>:</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>Z</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>Z</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow></mfrac></mrow><mi>:</mi><mo>=</mo><msup><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi>α</mi><mi>:</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>Z</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>=</mo><mn>4</mn><mi>π</mi><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo>=</mo><mn>3</mn><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>A</mi><mi>t</mi><mi>o</mi><mi>m</mi></mrow></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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