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-   -   Kronig-Penney model (attractive potential) (http://physicshelpforum.com/atomic-solid-state-physics/12361-kronig-penney-model-attractive-potential.html)

 essil Dec 29th 2016 06:53 PM

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.

 Woody Jan 2nd 2017 04:30 AM

<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)

 essil Jan 2nd 2017 08:05 AM

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.

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