# Dirac delta function

1. Jul 12, 2005

### cyberdeathreaper

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. Jul 12, 2005

### CarlB

Dear cyberdeathreaper,

It is a general property of delta functions that:

$$\int_{-\infty}^{\infty} f(p') \delta(p-p') dp' = f(p)$$

This formula is used in what you have written.

Carl

Last edited: Jul 12, 2005
3. Jul 12, 2005

### cyberdeathreaper

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.