The wavefunction of a particle moving inside a one dimensional box of length L is non-zero only for 0<x<L.(adsbygoogle = window.adsbygoogle || []).push({});

The normalised wavefunction is given by:

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

Is this wavefunction an eigenfunction of the x-component of the momentum operator [itex]\vec p = -i\hbar \vec \nabla[/itex]

My work:

I computed the partial derivative of [itex]\psi[/tex] with respect to 'x'. I got:

[tex]\frac{\partial \psi}{\partial x} = \sqrt{\frac{2}{L}}\left(\frac{n\pi}{L}\right)\cos \frac{n\pi x}{L}[/tex]

I don't think it is an eigenfunction of the operator but I don't know how to justify my answer. Help needed...

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# Homework Help: Verify whether eigenfunction or not?

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