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Display information for equation id:math.2561.3 on revision:2561

* Page found: Das ideale Bosegas (eq math.2561.3)

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Das ideale Bosegas Eq: math.2561.3

Hash: 353d577f4d03017830cc0cda0c6c150f

TeX (original user input):

\begin{align}
  & P\left( {{N}_{1}},{{N}_{2}},... \right)={{Y}^{-1}}\exp \left( -\beta \left( {{N}_{j}}{{E}_{j}}-\mu {{N}_{j}} \right) \right)=\prod\limits_{j=1}^{l}{{}}\left( 1-{{t}_{j}} \right){{t}_{j}}^{{{N}_{j}}}=\prod\limits_{j=1}^{l}{{}}p\left( {{N}_{j}} \right) \\ 
 & (separiert) \\ 
 &  \\ 
 & p\left( {{N}_{j}} \right)=\left( 1-{{t}_{j}} \right){{t}_{j}}^{{{N}_{j}}}=\left( 1-\exp \left( \beta \left( \mu -{{E}_{j}} \right) \right) \right)\exp \left( -\beta \left( {{N}_{j}}{{E}_{j}}-\mu {{N}_{j}} \right) \right) \\ 
 & 1-\exp \left( \beta \left( \mu -{{E}_{j}} \right) \right):={{e}^{{{\Psi }_{j}}}} \\ 
 & p\left( {{N}_{j}} \right)={{e}^{{{\Psi }_{j}}}}\exp \left( -\beta \left( {{N}_{j}}{{E}_{j}}-\mu {{N}_{j}} \right) \right) \\ 
\end{align}

TeX (checked):

{\begin{aligned}&P\left({{N}_{1}},{{N}_{2}},...\right)={{Y}^{-1}}\exp \left(-\beta \left({{N}_{j}}{{E}_{j}}-\mu {{N}_{j}}\right)\right)=\prod \limits _{j=1}^{l}{}\left(1-{{t}_{j}}\right){{t}_{j}}^{{N}_{j}}=\prod \limits _{j=1}^{l}{}p\left({{N}_{j}}\right)\\&(separiert)\\&\\&p\left({{N}_{j}}\right)=\left(1-{{t}_{j}}\right){{t}_{j}}^{{N}_{j}}=\left(1-\exp \left(\beta \left(\mu -{{E}_{j}}\right)\right)\right)\exp \left(-\beta \left({{N}_{j}}{{E}_{j}}-\mu {{N}_{j}}\right)\right)\\&1-\exp \left(\beta \left(\mu -{{E}_{j}}\right)\right):={{e}^{{\Psi }_{j}}}\\&p\left({{N}_{j}}\right)={{e}^{{\Psi }_{j}}}\exp \left(-\beta \left({{N}_{j}}{{E}_{j}}-\mu {{N}_{j}}\right)\right)\\\end{aligned}}

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\begin{aligned} P (N_{1}, N_{2}, . . .) = Y^{- 1} \exp (- β (N_{j} E_{j} - μ N_{j})) = \prod_{j = 1}^{l} (1 - t_{j}) {t_{j}}^{N_{j}} = \prod_{j = 1}^{l} p (N_{j}) \\ (s e p a r i e r t) \\ p (N_{j}) = (1 - t_{j}) {t_{j}}^{N_{j}} = (1 - \exp (β (μ - E_{j}))) \exp (- β (N_{j} E_{j} - μ N_{j})) \\ 1 - \exp (β (μ - E_{j})) : = e^{Ψ_{j}} \\ p (N_{j}) = e^{Ψ_{j}} \exp (- β (N_{j} E_{j} - μ N_{j})) \end{aligned}

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In Mathematica:

Identifiers

$P$

$N_{1}$

$N_{2}$

$Y$

$β$

$N_{j}$

$E_{j}$

$μ$

$N_{j}$

$j$

$l$

$t_{j}$

$t_{j}$

$N_{j}$

$j$

$l$

$p$

$N_{j}$

$s$

$e$

$p$

$a$

$r$

$i$

$e$

$r$

$t$

$p$

$N_{j}$

$t_{j}$

$t_{j}$

$N_{j}$

$β$

$μ$

$E_{j}$

$β$

$N_{j}$

$E_{j}$

$μ$

$N_{j}$

$β$

$μ$

$E_{j}$

$e$

$Ψ_{j}$

$p$

$N_{j}$

$e$

$Ψ_{j}$

$β$

$N_{j}$

$E_{j}$

$μ$

$N_{j}$

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