- #1

- 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):

$$cos(ka) = cos(\beta b)cos(\alpha (a-b))-\frac{\alpha ^2 + \beta ^2}{2\alpha \beta} sin(\beta b) sin(\alpha (a-b)) $$

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.

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):

$$cos(ka) = cos(\beta b)cos(\alpha (a-b))-\frac{\alpha ^2 + \beta ^2}{2\alpha \beta} sin(\beta b) sin(\alpha (a-b)) $$

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.

Last edited: