# Virial Theorem

1. Dec 1, 2009

### Void123

1. The problem statement, all variables and given/known data

I must prove that:

$$\frac{d}{dt}<xp> = 2<T> - <x\frac{dV}{dX}>$$

And use the virial theorem to prove that $$<T> = <V>$$

2. Relevant equations

$$2<T> = <x\frac{dV}{dX}>$$

$$\frac{d}{dt}<Q> = \frac{i}{h(bar)}<[H, Q]> + <\frac{\partial Q}{\partial t}>$$

Where Q on the right side is an operator, as well as H.

3. The attempt at a solution

Do I just plug in $$\frac{d}{dt}<xp>$$ into the general equation?

Thanks.

2. Dec 2, 2009

### kuruman

In the second equation that you posted, replace Q with xp and H with

$$-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2}+V(x)$$

and expand the commutator.