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Homework Help: Virial Theorem

  1. Dec 1, 2009 #1
    1. The problem statement, all variables and given/known data

    I must prove that:

    [tex]\frac{d}{dt}<xp> = 2<T> - <x\frac{dV}{dX}>[/tex]

    And use the virial theorem to prove that [tex]<T> = <V>[/tex]

    2. Relevant equations

    [tex]2<T> = <x\frac{dV}{dX}>[/tex]

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

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

    3. The attempt at a solution

    Do I just plug in [tex]\frac{d}{dt}<xp>[/tex] into the general equation?

  2. jcsd
  3. Dec 2, 2009 #2


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    Science Advisor
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    Gold Member

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

    [tex]-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2}+V(x)[/tex]

    and expand the commutator.
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