Physics Help Forum Kronig-Penney model (attractive potential)

 Atomic and Solid State Physics Atomic and Solid State Physics Help Forum

 Dec 29th 2016, 07:53 PM #1 Junior Member   Join Date: Dec 2016 Posts: 2 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.
 Jan 2nd 2017, 05:30 AM #2 Senior Member     Join Date: Jun 2016 Location: England Posts: 642 Your Smiley had been included in the link you posted (so it doesn't work), Here is the corrected link: 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 05:34 AM.
 Jan 2nd 2017, 09:05 AM #3 Junior Member   Join Date: Dec 2016 Posts: 2 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 09:33 AM.

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### kronig penney model in solid state physics

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