# Blackbody radiation - stat mech

we have a hollow cubical box with sides of length a with perfectly conducting walls, such that the electric field tangential to the surfaces of the walls must be zero. we need to show that the system of standing waves:
Ex = Ax*cos(Kx*x)*sin(Ky*y)*sin(Kz*z)*exp(iwt)
Ey = Ax*sin(Kx*x)*cos(Ky*y)*sin(Kz*z)*exp(iwt)
Ez = Ax*sin(Kx*x)*sin(Ky*y)*cos(Kz*z)*exp(iwt)

satisfies the wave equation in 3-d. I can do this. We also need to show that they satisfy the condition that div(E)=0 (I think this is because there is no charge density in the box) provided that there are two independent polarisations for light.
just doing algebra I can get the expression (Kx*Ax + Ky*Ay + Kz*Az) = 0 , but I'm not sure how this connects to light having two independent polarisations (or in fact what it means for light to have two independent polarisiations). any hlpful hints would be appreciated.

Sachi

For a given $$(K_x,K_y,K_z)$$, you can think of the solution to the equation you derived as a plane in the 3d space $$(A_x , A_y , A_z )$$. How many independent directions are there on such a plane?