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Homework Statement
What is the correct interpretation of
[tex] < \frac{\partial {A}}{\partial t} >[/tex], where A is an operator?
Homework Equations
for a wave function [tex]\phi[/tex] and operator A,
[tex]<A> = \int_{V}\phi^{*}(A\phi)dV[/tex]
The Attempt at a Solution
I thought it could mean
[tex] < \frac{\partial {A}}{\partial t} > = \int_{V}\phi^{*}\frac{\partial}{\partial t}(A\phi)dV[/tex]
but then again it might mean
[tex] < \frac{\partial {A}}{\partial t} > = \int_{V}\phi^{*}(\frac{\partial A}{\partial t})(\phi)dV[/tex].
I read an article saying that operators are associative. But, when I think about the operators [tex]t[/tex] and [tex]\frac{\partial}{\partial t}[/tex], then,
[tex]\frac{\partial}{\partial t}\left(t\phi\right) = t\frac{\partial\phi}{\partial t} + \phi \neq \left(\frac{\partial t}{\partial t}\right)\phi = \phi[/tex]
any thoughts?