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hi i was reading a textbook and this statement puzzled me. it stated that [tex]\frac{d}{dt}<A>=\frac{1}{ih}[A_{op},H] if \frac{\partial A_{op}}{ \partial t}=0 [/tex].

i was wanting to prove this and hence show that if Aop commutes A is a constant of motion and can be a good quantum number.

I get that: H is the hamiltonian expressed as follows: [tex](H\phi)=i\hbar\frac{\partial \phi}{\partial t}[/tex] , <A> is the expectation value: [tex]<A>=\int{\phi^*A_{op}\phi d\tau} [/tex] and [A_{op},H] is the commutator [tex] (A_{op}H-HA_{op}) [/tex] and this equals zero when it commutes. However i can't put it together to get the above equation. can someone show me how to do it please?

i was wanting to prove this and hence show that if Aop commutes A is a constant of motion and can be a good quantum number.

I get that: H is the hamiltonian expressed as follows: [tex](H\phi)=i\hbar\frac{\partial \phi}{\partial t}[/tex] , <A> is the expectation value: [tex]<A>=\int{\phi^*A_{op}\phi d\tau} [/tex] and [A_{op},H] is the commutator [tex] (A_{op}H-HA_{op}) [/tex] and this equals zero when it commutes. However i can't put it together to get the above equation. can someone show me how to do it please?

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