# Derivation of momentum operator / origin of -ih d/dx

## Homework Statement

In the derivation of the momentum operator: Why is this equal?

## Homework Equations

[PLAIN]http://img268.imageshack.us/img268/4575/momentumoperatorderivat.png [Broken]

## The Attempt at a Solution

I thought maybe the integral is executed, but the integral sign stays.
One p vanishes, the momentum operator itself shows up.
You would really expect this in a derivation of p, but dp stays.

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vela
Staff Emeritus
$$p \exp\left(\frac{ipx}{\hbar}\right) = \frac{\hbar}{i}\frac{\partial}{\partial x}\exp\left(\frac{ipx}{\hbar}\right)$$