Is the Expectation Value of Uncertainty Constant in Time?

[capandbells]

Homework Statement

Show that, if [H,A] = 0 and dA/dt = 0, then <&Delta;A> is constant in time.

Homework Equations

d<A>/dt = <i/ℏ[H,A] + dA/dt>

The Attempt at a Solution

I am trying to use the above equation to show that d<&Delta;A>/dt is 0, and I can get to d&Delta;A/dt = 0, but I can't figure out how to compute [H,&Delta;A]. The only thing I can think of is that since &Delta; A is just a function of A and A commutes with H, then &Delta; A also commutes with H, but I can't find a theorem that says that.

 

[dextercioby]

What's the definition of $\delta A$ ? Then differentiate it wrt time and use Heisenberg's equation of motion.

 

[capandbells]

Sorry, I don't know Heisenberg's equation of motion. We haven't gone over it in class and it doesn't show up in my book until much later.

 

[dextercioby]

What is the name of the equation you placed under <Relevant equations> ?