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I have this problem to do, and its only worth one mark which makes me think it must be easy, but our lecturer has not taught us very well at all, never explains anything.

Anyway, there's a particle confined in an infinite potential well within the region -L/2 < x < L/2, where the potential is zero. At a certain time it is described by the wavefunction:

psi(x) = Acos(pi.x/L) + 2Asin(2pi.x/L).[where A = sqrt(2/5L)]

I am supposed to write down psi(x) in terms of the eigenfunctions of energy.

First off, I don't really know what an eigenfunction of energy is, or is supposed to look like, so i dont know what i am supposed to be writing psi(x) in terms of. All i have really done with this question is write down the time-independent Schrodinger equation with the V(x) term missing, since the potential is zero, so i have:

-H/2m.(d^2/dx^2)psi(x) = E(psi(x)) [where H = h/2 pi]

Other than that i have just aimlessly messed around with the equation above.

Can anybody help me out? I am desperate for help with this stuff, its starting to frustrate me now.

Thank you.

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# Homework Help: A (probably simple) quantum problem - energy eigenfunctions?

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