Consider the equation of motion for the expectation value of an operator $A$ $$\frac{d\langle A\rangle}{dt} = \frac{1}{i\hbar}\langle [A,H]\rangle + \left \langle \frac{\partial A}{\partial t} \right \rangle \, .$$ I am confused with the second term, $\langle \partial A / \partial t \rangle$. Why does $\langle \partial A / \partial t \rangle$ vanish for observables?
if the observable $A$ does not depend explicitly on time, the term $\langle \frac{\partial A}{\partial t}\rangle$ will vanish
-- Zettili's Quantum Mechanics Book
What does it really mean when $A$ is $X$ or $P_x$ for example? If $$\hat P_x= -i\hbar\frac{\partial }{\partial x}$$ then $$ \left \langle \frac{\partial \hat P_x}{\partial t} \right \rangle = \left \langle -i\hbar\frac{\partial}{\partial t} \left( \frac{\partial }{\partial x} \right) \right \rangle = ? $$ Why does it vanish and what does it really mean?
[I am very confused with the concept of the expectation value of an operator. I have checked these:
