# Expectation value of uncertainty

1. Oct 15, 2011

### capandbells

1. The problem statement, all variables and given/known data
Show that, if [H,A] = 0 and dA/dt = 0, then <&Delta;A> is constant in time.

2. Relevant equations
d<A>/dt = <i/ℏ[H,A] + dA/dt>

3. 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.

2. Oct 16, 2011

### dextercioby

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

3. Oct 16, 2011

### 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.

4. Oct 17, 2011

### dextercioby

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