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Display information for equation id:math.2273.97 on revision:2273
* Page found: Vorurteilsfreie Schätzung des statistischen Operators zu einem festen Zeitpunkt (eq math.2273.97)
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Hash: b6e1d48bc5018c8a32a0fe03941f25b8
TeX (original user input):
\begin{align}
& k\sum\limits_{\alpha }{\frac{1}{Z}\frac{\partial Z}{\partial {{h}_{\alpha }}}d{{h}_{\alpha }}}=k\sum\limits_{\alpha }{\frac{1}{Z}\operatorname{Tr}\left( \frac{\partial }{\partial {{h}_{\alpha }}}{{\operatorname{e}}^{-\sum\limits_{\nu }{{{\lambda }_{\nu }}{{G}_{\nu }}}}} \right)d{{h}_{\alpha }}} \\
& =k\sum\limits_{\alpha }{\operatorname{Tr}\left( -\sum\limits_{\nu }{{{\lambda }_{\nu }}}\frac{\partial {{G}_{\nu }}}{\partial {{h}_{\alpha }}}R \right)d{{h}_{\alpha }}} \\
& =-k\sum\limits_{\alpha ,\nu }{{{\lambda }_{\nu }}\left\langle \frac{\partial {{G}_{\nu }}}{\partial {{h}_{\alpha }}} \right\rangle d{{h}_{\alpha }}}
\end{align}
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