Understanding Operators & Observables: Averages & Variance

[Feynmanfan]

I have trouble understanding operators and observables:

Does <A> the average value of an observable and the variance depend on the state of the system? What does it have to do with the Hamiltonian?

Thanks!

 

[dextercioby]

Basically none.Yes,both the variance and the expectation value/average depend upon the quantum state.

Daniel.

 

[shyboy]

This is too general question. With respect to Hamiltonian there are two types of operators- those which commute and those which does not commute with Hamiltonian.
If we have a time independent Hamiltonian, then those operators which commute with it will have their average value constant.