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Virial theorem, hamiltonian

  1. Apr 17, 2013 #1
    1. The problem statement, all variables and given/known data
    A quantum particle, i.e. a particle obeying Schrodinger equation and
    moving in one dimension experiences a potential ˆV (x). In a stationary state
    of this system show that

    ⟨x∂/∂x(ˆV(x)⟩ = ⟨ˆp2/2m⟩

    Hint: Consider the time dependence of ⟨ˆxˆp⟩.


    2. Relevant equations

    I was told the answer would be some variation of the virial theorem as proven here - http://www7b.biglobe.ne.jp/~kcy05t/viriproof.html#qua

    but i do not get the connection

    3. The attempt at a solution

    I was thinking of doing it as per the hint - by trying to find the d/dt of <^x^p>

    (something prefixed by a "^" signifies an operator - i.e "^p" is the momentum operator etc
     
  2. jcsd
  3. Apr 18, 2013 #2
    just go with d/dt<x.p> and prove that <x.p> for stationary state is independent of time.Use the formula from the reference you already have for d/dt<O>,where O is some operator.
    EDIT-wait,does not that reference already has solution.
     
    Last edited: Apr 18, 2013
  4. Apr 18, 2013 #3
    hi

    so i am confused now - does the reference already have the soln - i dont even see it !!
     
  5. Apr 18, 2013 #4
    hmm... any other hints or suggestions.

    Thanks
     
  6. Apr 20, 2013 #5
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