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Display information for equation id:math.2507.47 on revision:2507
* Page found: Das ideale Gas (eq math.2507.47)
(force rerendering)Occurrences on the following pages:
Hash: dceb12c8a72c0b7df84b44d50cc0398f
TeX (original user input):
\begin{align}
& \Psi =-\bar{N} \\
& \beta =\frac{3\bar{N}}{2U} \\
& \alpha =-\ln \frac{Y}{V\Phi \left( \beta \right)}=\ln \frac{V{{\left( \frac{4\pi mU}{3\bar{N}{{\hbar }^{2}}} \right)}^{\frac{3}{2}}}}{{\bar{N}}} \\
\end{align}
TeX (checked):
{\begin{aligned}&\Psi =-{\bar {N}}\\&\beta ={\frac {3{\bar {N}}}{2U}}\\&\alpha =-\ln {\frac {Y}{V\Phi \left(\beta \right)}}=\ln {\frac {V{{\left({\frac {4\pi mU}{3{\bar {N}}{{\hbar }^{2}}}}\right)}^{\frac {3}{2}}}}{\bar {N}}}\\\end{aligned}}
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MathML (2.275 KB / 473 B) :
<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"><mi>Ψ</mi><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mover><mi>N</mi><mo>¯</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>β</mi><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>3</mn><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>U</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>α</mi><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi>ln</mi><mo>⁡</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>Y</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>V</mi><mi>Φ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>β</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mi>ln</mi><mo>⁡</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>V</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi><mi>m</mi><mi>U</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>3</mn><mover><mi>N</mi><mo>¯</mo></mover><msup><mi alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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