Proving 2<T> = <x\frac{dV}{dX}> and Virial Theorem

[Void123]

Homework Statement

I must prove that:

\frac{d}{dt}&lt;xp&gt; = 2&lt;T&gt; - &lt;x\frac{dV}{dX}&gt;

And use the virial theorem to prove that &lt;T&gt; = &lt;V&gt;

Homework Equations

2&lt;T&gt; = &lt;x\frac{dV}{dX}&gt;

\frac{d}{dt}&lt;Q&gt; = \frac{i}{h(bar)}&lt;[H, Q]&gt; + &lt;\frac{\partial Q}{\partial t}&gt;

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

The Attempt at a Solution

Do I just plug in \frac{d}{dt}&lt;xp&gt; into the general equation?

Thanks.

 

[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.