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Homework Help: Dirac delta function

  1. Jul 12, 2005 #1
    Can someone help me understand the transition between these two steps?
    [tex]
    <x> = \iint \Phi^* (p',t) \delta (p - p') \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t) \right) dp' dp
    [/tex]
    =
    [tex]
    <x> = \int \Phi^* (p,t) \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t) \right) dp
    [/tex]

    Assume the integrals go from -infinity to +infinity, and assume the delta function is the Dirac delta function.
     
    Last edited: Jul 12, 2005
  2. jcsd
  3. Jul 12, 2005 #2

    CarlB

    User Avatar
    Science Advisor
    Homework Helper

    Dear cyberdeathreaper,

    It is a general property of delta functions that:

    [tex]\int_{-\infty}^{\infty} f(p') \delta(p-p') dp' = f(p)[/tex]

    This formula is used in what you have written.

    Carl
     
    Last edited: Jul 12, 2005
  4. Jul 12, 2005 #3
    Thanks, I knew it was related to that. I just wasn't sure if it applied for functions of more than one variable or not.
     
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