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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.

[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.

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