I would like to solve these two simultaneous equations for $E_p(k)$ provided that $p\neq \pm n\pi$, where $n$ is an integer:
3 K*d^2 + Sqrt[C1^2 + 4*C2^2*Cos[k/2]^2 + 4*C1*C2*Cos[k/2]*Cos[p]]==Ep; C1*Sin[p*n] + 2*C2*Cos[k/2]*Sin[p*(n + 1)]==0;
I've tried declaring $p\neq \pm n\pi$ within an NSolve in place of inequalities and I've tried deleting the undesired $p$ values posthumously using DeleteCases, both to no avail. Here are the constants used too:
n = 3; t = 2.5; a = 6.31; K = 49.7; d = 0.1; C1 = -t - 2*a*d; C2 = -t + a*d;
Any help would be greatly appreciated, thanks!