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Hi!

I am having some difficulty in finding a definition about some kind of reverse operation (integration) of a derivative with respect to an operator which may defined as follows.

Suppose we have a function of n, in general non commuting, operators [tex] H(q_1 ,..., q_n) [/tex] then differentiation with respect to one of them can be defined as,

[tex]

\begin{equation}

\frac{\partial H}{\partial q_i}=\lim_{\lambda \rightarrow 0}\frac{\partial H}{\partial \lambda}(q_1 ,...,q_i +\lambda,..., q_n)

\end{equation}

[/tex]

I have found the above definition in the paper,"Exponential Operators and Parameter Differentiation in Quantum Physics", R. M. Wilcox, J. Math. Phys. 8, 962 (1967) for which a book by Louisell, "Radiation and noise in Quantum Electronics" is cited. Unfortunately I do not have access to that book at the moment where there is a good chance I can find what I am looking for.

I would appreciate if someone could provide a definition, if there is one, and in addition point out some references for further studying.

Thank you in advance.

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# Integration on operators

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