Hi, I've been working on writing the wave function in terms of momentum eigenfunctions. The only problem I have with the derivation is the last step, which allows me to write:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Psi(x) = \int^{\infty}_{-\infty} \phi(p)u_{p}(x)dp[/tex]

where

[tex]

u_{p}(x) = \frac{1}{\sqrt{2\pi\hbar}}e^{\frac{ipx}{\hbar}}

[/tex]

What allows me to do so? I haven't found a way to prove this. I know that I can write the wave function like so:

[tex] \Psi(x) = \sum c_{n}u_{n}[/tex]

as long as i have a complete basis, but how do I go from this to the integral? Or is this irrelevant? his is on Griffiths QM Ed2 on page 104, but all he says is "Any (square-integratable) function f(x) can be written in the form [what i showed above]" I haven't found anywhere where he proves this or expects one to prove this in the problems.

Can someone please tell me how to get started on proving this? If anyone can help me out with this one I would appreciate it greatly.

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# Homework Help: Why can we rewrite the wave function like so:

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