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Display information for equation id:math.2202.1 on revision:2202
* Page found: Kurzer historischer Überblick (eq math.2202.1)
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Hash: d0a1564bfdc7b01d6ab362c3af9843c3
TeX (original user input):
\underbrace{w\left( v \right)}_{\begin{align}
& \text{Wahrscheinlichkeit beim } \\
& \text{Reingreifen in ein} \\
& \text{Gas ein Teilchen mit} \\
& \left| \underline{v} \right|\text{=}v\text{ zu finden } \\
\end{align}}=4\pi {{\left( \frac{m}{2\pi {{k}_{B}}T} \right)}^{3/2}}{{v}^{2}}\underbrace{\exp \left( -\frac{m{{v}^{2}}}{2{{k}_{B}}T} \right)}_{\begin{smallmatrix}
\text{legt einen Abschneideparameter} \\
\text{kT}\triangleq \text{thermischen Energie fest}
\end{smallmatrix}}
TeX (checked):
\underbrace {w\left(v\right)} _{\begin{aligned}&{\text{Wahrscheinlichkeit beim }}\\&{\text{Reingreifen in ein}}\\&{\text{Gas ein Teilchen mit}}\\&\left|{\underline {v}}\right|{\text{=}}v{\text{ zu finden }}\\\end{aligned}}=4\pi {{\left({\frac {m}{2\pi {{k}_{B}}T}}\right)}^{3/2}}{{v}^{2}}\underbrace {\exp \left(-{\frac {m{{v}^{2}}}{2{{k}_{B}}T}}\right)} _{\begin{smallmatrix}{\text{legt einen Abschneideparameter}}\\{\text{kT}}\triangleq {\text{thermischen Energie fest}}\end{smallmatrix}}
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MathML (3.017 KB / 637 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><mi>w</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>v</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><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"><mtext>Wahrscheinlichkeit beim </mtext></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>Reingreifen in ein</mtext></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>Gas ein Teilchen mit</mtext></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="ORD"><munder><mi>v</mi><mo>_</mo></munder></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mtext>=</mtext></mrow><mi>v</mi><mrow data-mjx-texclass="ORD"><mtext> zu finden </mtext></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mrow></munder><mo>=</mo><mn>4</mn><mi>π</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>B</mi></mrow></msub><mi>T</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>3</mn><mo>/</mo><mn>2</mn></mrow></mrow></msup><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>B</mi></mrow></msub><mi>T</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mrow data-mjx-texclass="ORD"><mtext>legt einen Abschneideparameter</mtext></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="ORD"><mtext>kT</mtext></mrow><mo>≜</mo><mrow data-mjx-texclass="ORD"><mtext>thermischen Energie fest</mtext></mrow></mtd></mtr></mtable></mrow></mrow></munder></mstyle></mrow></math>
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