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Display information for equation id:math.2578.48 on revision:2578
* Page found: Ferromagnetismus (eq math.2578.48)
(force rerendering)Occurrences on the following pages:
Hash: ced9bdcca8f7ac21491ed91d71435925
TeX (original user input):
\begin{align}
& U=-\frac{\partial }{\partial \beta }\ln {{Z}^{N}}=-N\frac{\partial }{\partial \beta }\ln \left[ 2\cosh \left( \frac{\beta \mu B}{2} \right) \right]=-\frac{N\mu B}{2}\frac{\sinh \left( \frac{\beta \mu B}{2} \right)}{\cosh \left( \frac{\beta \mu B}{2} \right)} \\
& U\left( T \right)=-\frac{N\mu B}{2}\tanh \left( \frac{\beta \mu B}{2} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&U=-{\frac {\partial }{\partial \beta }}\ln {{Z}^{N}}=-N{\frac {\partial }{\partial \beta }}\ln \left[2\cosh \left({\frac {\beta \mu B}{2}}\right)\right]=-{\frac {N\mu B}{2}}{\frac {\sinh \left({\frac {\beta \mu B}{2}}\right)}{\cosh \left({\frac {\beta \mu B}{2}}\right)}}\\&U\left(T\right)=-{\frac {N\mu B}{2}}\tanh \left({\frac {\beta \mu B}{2}}\right)\\\end{aligned}}
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MathML (3.389 KB / 448 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><mi>U</mi><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>β</mi></mrow></mrow></mfrac></mrow><mi>ln</mi><mo>⁡</mo><msup><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><mo>=</mo><mo>−</mo><mi>N</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>β</mi></mrow></mrow></mfrac></mrow><mi>ln</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>2</mn><mi>cosh</mi><mo>⁡</mo><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"><mi>β</mi><mi>μ</mi><mi>B</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>μ</mi><mi>B</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>sinh</mi><mo>⁡</mo><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"><mi>β</mi><mi>μ</mi><mi>B</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>cosh</mi><mo>⁡</mo><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"><mi>β</mi><mi>μ</mi><mi>B</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>U</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>μ</mi><mi>B</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mi>tanh</mi><mo>⁡</mo><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"><mi>β</mi><mi>μ</mi><mi>B</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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