So, I'm completing the Kronig-Penney model, a quantum mechanics problem, from scratch. I obtained four equations that must be held true, and I wrote them as a matrix where the determinant is equal to zero.
I know this much to be correct, as I arrived at the same Matrix as Wikipedia:
I also know that this matrix is satisfied when a specific transcendental equation is satisfied. The equation is given below:
Transcendental Equation (Solution)
I know there must be a way to solve the matrix and arrive at this equation, but I haven't had success. I have tried using MATLAB, but am told that no explicit solutions can be found (which is fine, but how do I find the implicit transcendental?).
I would really appreciate anyone's input on whether I can solve this problem, with coding or without.
Thank you, everyone, for your help :)