- #1

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[tex]\psi = \sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L}[/tex]

With boundary conditions 0<x<L.

When I compute the expectation value for the momentum like this:

[tex]\overline{p_x} = \int_0^L \sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L} \left(-i\hbar \frac{\partial}{\partial x}\right)\sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L} dx[/tex]

On evaluation I get:

[tex]\frac{2n\pi \hbar}{iL^2}\left[\frac{L}{2n\pi}\sin^2 \frac{n\pi x}{L}\right]_0^L = 0[/tex]

Why is the expectation value of the momentum Zero?