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How do we find the eigenfunctions if we are given the wavefunction? I have a wave function at time = 0 and it is of a *free* particle and I need to find the wave function at a later time t. I did :

[tex]\Psi(x,t)=\Psi(x,0)*e^{-iHt/hbar}[/tex] then

[tex]\Psi(x,t)=\sum_{n}(<\phi_{n}|\Psi(x,0)> |\phi_{n}> e^{-iE_{n}t/hbar})[/tex]

I have [tex]\Psi(x,0)[/tex] so the only thing I need to know is [tex]\phi_{n}[/tex] which are the eigenfunctions and I have no idea how to do this. I solved Schroginger's equation and got [tex]\Psi(x)=Ae^{ikx}+Be^{-ikx}[/tex], where k[tex]^{2}[/tex]=[tex]\frac{2mE}{hbar^{2}}[/tex], and the particle is totally free.

thanks in advance.

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# Homework Help: How to find eigenfunctions given the wave function?

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