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QM: Force

  1. Feb 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi

    In QM we define the force operator F as (in the Heisenberg picture)
    [tex]
    F = \frac{1}{i\hbar}[p, H] + (d_t F)(t)
    [/tex]
    What I can't understand is that usually (actually, always) we write
    [tex]
    F = \frac{1}{i\hbar}[p, H]
    [/tex]
    and neglegt the last time derivative. How can we be so certain that the force is time-independent?

    Best regards,
    Niles.
     
  2. jcsd
  3. Feb 24, 2012 #2

    vela

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    Shouldn't the second term be the derivative of p, not F?
     
  4. Feb 25, 2012 #3
    You are right, it is the derivative of p. But the velocity is not necessarily time-independent?
     
  5. Feb 25, 2012 #4

    vela

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    You're looking about the derivative of the operator itself, not the derivative of the momentum of the particle. Second, ∂p/∂t ≠ 0 only if the operator has an explicit time dependence.
     
  6. Feb 25, 2012 #5
    You are right, thanks for that. In that case it is obvious that the last term is zero.

    Best regards,
    Niles.
     
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