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Old Dec 29th 2016, 06:53 PM   #1
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Kronig-Penney model (attractive potential)

Hi all!

Can anyone confirm (or point me to literature) that the dispersion relation for the attractive Kronig-Penney potential is correctly given on Wikipedia (https://en.wikipedia.org/wiki/Partic...onal_lattice):

$$cos(ka)=cos(βb)cos(α(a−b))−\frac{α^2+β^2}{2αβ}si n(βb)sin(α(a−b))$$

I have been unsuccessful at calculating the determinant (also given on Wikipedia) despite multiple tries, and was unable to find literature which deals with the attractive variant of the potential.
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Old Jan 2nd 2017, 04:30 AM   #2
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Your Smiley had been included in the link you posted (so it doesn't work),
Here is the corrected link:
<Particle in a one dimensional lattice>

I'm sorry but I will have to leave the maths to someone else,
it is beyond my limited abilities.

There must be some mathematician out there who is willing give it a go...
(or have you all totally addled your brains in the new-year celebrations)

Last edited by Woody; Jan 2nd 2017 at 04:34 AM.
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Old Jan 2nd 2017, 08:05 AM   #3
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Happy New Years! Check the appendix here:

https://kdf.mff.cuni.cz/vyuka/konden...onigPenney.pdf

It gives instructions for calculating the determinant of the variant of the potential with potential barriers. I've tried to follow the instructions for my (attractive) case but I can't see it through to the end.

Last edited by essil; Jan 2nd 2017 at 08:33 AM.
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