# Kronig-Penney model (attractive potential)

#### essil

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/Particle_in_a_one-dimensional_lattice):

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

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

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)

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