1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dirac delta function

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

    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


    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.

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Dirac delta function
  1. Dirac delta function (Replies: 1)

  2. Dirac Delta Function (Replies: 9)