Kronig-Penney model (attractive potential)

Dec 2016
2
0
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.
 
Jun 2016
1,182
549
England
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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