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In the context of observables in QM the rate of change of the In the contest of observables in QM the rate of change of the expectation value of an observable A is defined by:

d<A>/dt= d< Y | A Y>/dt = < d Y/dt | A Y > + < Y | dA/dt . Y > + < Y | A dY/dt>

My question is about the second term (< Y | dA/dt . Y >), is it mathematically correct to differentiate an operator!? Can anyone explain to me what's going on? After all d/dt is an operator that works on a function or on another operator as well? I am confused.

d<A>/dt= d< Y | A Y>/dt = < d Y/dt | A Y > + < Y | dA/dt . Y > + < Y | A dY/dt>

My question is about the second term (< Y | dA/dt . Y >), is it mathematically correct to differentiate an operator!? Can anyone explain to me what's going on? After all d/dt is an operator that works on a function or on another operator as well? I am confused.

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