Understanding Transition btwn Steps of Dirac Delta Function

[cyberdeathreaper]

Can someone help me understand the transition between these two steps?
<br /> &lt;x&gt; = \iint \Phi^* (p&#039;,t) \delta (p - p&#039;) \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t) \right) dp&#039; dp<br />
=
<br /> &lt;x&gt; = \int \Phi^* (p,t) \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t) \right) dp<br />

Assume the integrals go from -infinity to +infinity, and assume the delta function is the Dirac delta function.

 

[CarlB]

Dear cyberdeathreaper,

It is a general property of delta functions that:

\int_{-\infty}^{\infty} f(p&#039;) \delta(p-p&#039;) dp&#039; = f(p)

This formula is used in what you have written.

Carl

 

[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.