(adsbygoogle = window.adsbygoogle || []).push({}); Particle in a BOX -- what are allowed momenta?

Ok I am trying to come up with the first five eigenfunctions for the particle in a box of size 2L. Now, I gave the appropriate initial conditions and get as a solution phi(x) = bcos(kx) + asin(kx). I said that phi(-L) = phi(L) = 0 which game me bcos(kL) + asin(kL) = 0 and bcos(kL) - asin(kL) = 0 . Upon solving them, I get that for n being odd, k = nPi/2L and for even n, k = nPi/L. Thus for odd n, phi(x) = asin(nPix/2L) and for even n, phi(x) = bcos(nPix/L). Now, I can easily plot these for n = 1,2,3,4,5 but I am also asked WHAT ARE THE allowed values of momenta.

Now, I managed to get the allowed values of energy since from the resulting differential equation, I defined E = (k^2)*(hbar^2)/2m. So clearly, once I have k for various n, I have E.

Now my question: How do I relate energy to momenta?

Also, the question says "DO NOT FORGET TO INCLUDE SYMMETRIC AND ANTISYMMETRIC EIGENFUNCTIONS in your plot" Do they mean even and odd or what?

I am desparate for help with this nagging issue.

student1938

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# Homework Help: Particle in a BOX - what are allowed momenta?

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