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Display information for equation id:math.2585.8 on revision:2585

* Page found: Paramagnetismus (eq math.2585.8)

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Paramagnetismus Eq: math.2585.8

Hash: 2c2ede34823f13ae2a0f4b383d4cdfdd

TeX (original user input):

\begin{align}

& M=\frac{N}{V}\sum\limits_{{{m}_{l}}=-l}^{l}{{}}\mu {{m}_{l}}{{Z}^{-1}}\exp \left( \beta \mu B{{m}_{l}} \right)=\frac{N}{V}\frac{1}{Z}\sum\limits_{{{m}_{l}}=-l}^{l}{{}}\mu {{m}_{l}}\exp \left( \beta \mu B{{m}_{l}} \right) \\

& =\frac{N}{V}\frac{1}{\beta }\frac{\partial }{\partial B}\ln Z \\

& =\frac{N}{V}\mu \left[ \left( l+\frac{1}{2} \right)\coth \left[ \beta \mu B\left( l+\frac{1}{2} \right) \right]-\frac{1}{2}\coth \left[ \frac{1}{2}\beta \mu B \right] \right] \\

\end{align}

TeX (checked):

{\begin{aligned}&M={\frac {N}{V}}\sum \limits _{{{m}_{l}}=-l}^{l}{}\mu {{m}_{l}}{{Z}^{-1}}\exp \left(\beta \mu B{{m}_{l}}\right)={\frac {N}{V}}{\frac {1}{Z}}\sum \limits _{{{m}_{l}}=-l}^{l}{}\mu {{m}_{l}}\exp \left(\beta \mu B{{m}_{l}}\right)\\&={\frac {N}{V}}{\frac {1}{\beta }}{\frac {\partial }{\partial B}}\ln Z\\&={\frac {N}{V}}\mu \left[\left(l+{\frac {1}{2}}\right)\coth \left[\beta \mu B\left(l+{\frac {1}{2}}\right)\right]-{\frac {1}{2}}\coth \left[{\frac {1}{2}}\beta \mu B\right]\right]\\\end{aligned}}

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\begin{aligned} M = \frac{N}{V} \sum_{m_{l} = - l}^{l} μ m_{l} Z^{- 1} \exp (β μ B m_{l}) = \frac{N}{V} \frac{1}{Z} \sum_{m_{l} = - l}^{l} μ m_{l} \exp (β μ B m_{l}) \\ = \frac{N}{V} \frac{1}{β} \frac{\partial}{\partial B} \ln Z \\ = \frac{N}{V} μ [(l + \frac{1}{2}) \coth [β μ B (l + \frac{1}{2})] - \frac{1}{2} \coth [\frac{1}{2} β μ B]] \end{aligned}

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Identifiers

$M$

$N$

$V$

$m_{l}$

$l$

$l$

$μ$

$m_{l}$

$Z$

$β$

$μ$

$B$

$m_{l}$

$N$

$V$

$Z$

$m_{l}$

$l$

$l$

$μ$

$m_{l}$

$β$

$μ$

$B$

$m_{l}$

$N$

$V$

$β$

$B$

$Z$

$N$

$V$

$μ$

$l$

$β$

$μ$

$B$

$l$

$β$

$μ$

$B$

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