Hmm. Not meaning to distract attention from the HW post preceding this, but here are some wave-functions for the 1D H.O. and H-atom. These are related to problems 6 and 8 (review).
I am not sure why, but I just LOVE the 1/sqrt(2) under the e{i phi}. How do you feel about it?
They may not be quite right, but let's try to establish and repair any errors through comments here. It is very helpful to have a "standard set" for these as part of our "common culture". If we all use the same, hopefully correct ones, in ongoing and upcoming problems, then, uh, well,... that is a good thing... right?
5 comments:
Zack, i recognize those wave functions and they look good. I am curious why you like the one over square root under the e to the 'i-phi' there, is it just because ;) or does it make something better for future problems? Its okay it its just because, haha.
For problem #6, I think "a" should go beneath the inflection point of psi-1, which looks like it corresponds to the node of psi-3, But, if you examine psi-3(a), (where x=a) you get a non zero negative number that is probably a lot less than 1. So its a possibility that "a" is close to the node of psi-3. Just a quick brain storm.
Hey Zack, I think you may have normalized your H.O. states incorrectly.
I think your phi_2 should be (2/Pi/a^2)^1/4 * 2x/a * Exp[-x^2/a^2]
psi_3 should be (2/Pi/a^2)^1/4 * 1/Sqrt[2] * (4x^2/a^2 - 1) * Exp[-x^2/a^2]
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Radially there are nodes at the origin for psi_210, psi_211 and psi_21-1.
Additionally psi_210 has nodes all along the x-y plane (includes origin of course).
psi_211 and psi_21-1 have nodes along the z-axis and azimuthal behavior I'll leave to someone else hehe.
jesse, didn't he just pull the a^2 out of the 1/4, and write it as root 'a'? maybe i missed a factor of a somewhere in there.
yeah he did, and I think that that's fine. It's the 2ish factors that are off for the normalization.
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