p6.626x1034js
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Homework Statement
What is the correct interpretation of
< \frac{\partial {A}}{\partial t} >, where A is an operator?
Homework Equations
for a wave function \phi and operator A,
<A> = \int_{V}\phi^{*}(A\phi)dV
The Attempt at a Solution
I thought it could mean
< \frac{\partial {A}}{\partial t} > = \int_{V}\phi^{*}\frac{\partial}{\partial t}(A\phi)dV
but then again it might mean
< \frac{\partial {A}}{\partial t} > = \int_{V}\phi^{*}(\frac{\partial A}{\partial t})(\phi)dV.
I read an article saying that operators are associative. But, when I think about the operators t and \frac{\partial}{\partial t}, then,
\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
any thoughts?