# Plotting the first Brillouin zone

I'm trying to plot the first Brillouin zone from an equation I solved for this case.

This is the code I used:

m1 = 10;
m2 = 150;
g1 = 2;
g2 = 1;
(* A = 2; *)
a = (m1*m2)/(g1 - g2)^2;
b = (2*g1*m1 + g1*m2 + g2*m2)/(g1 - g2)^2;
c = -1/(g1 - g2) * cos[k*A] + 1;
w[k_] = a*w^4 + b*w^2 + c;
sol = Simplify[Solve[w[k] == 0, w]]
Plot[sol, {k, -Pi/A, Pi/A}]


The first Brillouin zone is defined for -π/A≤k≤-π/A, where A is the lattice constant.

I've tried both giving A a value (for example 2) and leaving it as it is, but in both cases I'm getting a blank plot.

Can't I do it this way, using symbols, or is my reasoning at fault?

• try A=2; Plot[Evaluate[ReIm@w /. sol], {k, -Pi/A, Pi/A}]? – kglr Jan 11 at 18:41
• The function still didn't plot – Plamus1 Jan 11 at 18:54
• Your function w[k] is not well defined. Check it. – Cesareo Jan 11 at 19:04
• Change cos[]to Cos[] . Function w[k] should be W[k] to avoid conflict with parameter w. – Ulrich Neumann Jan 11 at 21:45
• – Michael E2 Jan 12 at 2:10