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* Page found: Verallgemeinerte kanonische Verteilung (eq math.930.78)

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Verallgemeinerte kanonische Verteilung Eq: math.940.78

Hash: b9c943d8614f7cf890acb9eb6a081cf4

TeX (original user input):

\begin{align}
  & \frac{\partial }{\partial {{\lambda }_{n}}}\left( \frac{\partial \Psi }{\partial {{\lambda }_{m}}} \right)=\frac{\partial }{\partial {{\lambda }_{m}}}\left( \frac{\partial \Psi }{\partial {{\lambda }_{n}}} \right) \\ 
 & \left( \frac{\partial \Psi }{\partial {{\lambda }_{m}}} \right)=\left\langle {{M}^{m}} \right\rangle \Rightarrow \frac{\partial }{\partial {{\lambda }_{n}}}\left( \frac{\partial \Psi }{\partial {{\lambda }_{m}}} \right)={{\eta }^{mn}} \\ 
 & \left( \frac{\partial \Psi }{\partial {{\lambda }_{n}}} \right)=\left\langle {{M}^{n}} \right\rangle \Rightarrow \frac{\partial }{\partial {{\lambda }_{m}}}\left( \frac{\partial \Psi }{\partial {{\lambda }_{n}}} \right)={{\eta }^{nm}} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {\partial }{\partial {{\lambda }_{n}}}}\left({\frac {\partial \Psi }{\partial {{\lambda }_{m}}}}\right)={\frac {\partial }{\partial {{\lambda }_{m}}}}\left({\frac {\partial \Psi }{\partial {{\lambda }_{n}}}}\right)\\&\left({\frac {\partial \Psi }{\partial {{\lambda }_{m}}}}\right)=\left\langle {{M}^{m}}\right\rangle \Rightarrow {\frac {\partial }{\partial {{\lambda }_{n}}}}\left({\frac {\partial \Psi }{\partial {{\lambda }_{m}}}}\right)={{\eta }^{mn}}\\&\left({\frac {\partial \Psi }{\partial {{\lambda }_{n}}}}\right)=\left\langle {{M}^{n}}\right\rangle \Rightarrow {\frac {\partial }{\partial {{\lambda }_{m}}}}\left({\frac {\partial \Psi }{\partial {{\lambda }_{n}}}}\right)={{\eta }^{nm}}\\\end{aligned}}

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\begin{aligned} \frac{\partial}{\partial λ_{n}} (\frac{\partial Ψ}{\partial λ_{m}}) = \frac{\partial}{\partial λ_{m}} (\frac{\partial Ψ}{\partial λ_{n}}) \\ (\frac{\partial Ψ}{\partial λ_{m}}) = ⟨ M^{m} ⟩ \Rightarrow \frac{\partial}{\partial λ_{n}} (\frac{\partial Ψ}{\partial λ_{m}}) = η^{m n} \\ (\frac{\partial Ψ}{\partial λ_{n}}) = ⟨ M^{n} ⟩ \Rightarrow \frac{\partial}{\partial λ_{m}} (\frac{\partial Ψ}{\partial λ_{n}}) = η^{n m} \end{aligned}

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Identifiers

$λ_{n}$

$Ψ$

$λ_{m}$

$λ_{m}$

$Ψ$

$λ_{n}$

$Ψ$

$λ_{m}$

$M$

$m$

$λ_{n}$

$Ψ$

$λ_{m}$

$η$

$m$

$n$

$Ψ$

$λ_{n}$

$M$

$n$

$λ_{m}$

$Ψ$

$λ_{n}$

$η$

$n$

$m$

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