# Quantized modes of EM field in a cubic cavity

I am trying to solve for Electric field modes in a cubic cavity with perfectly reflecting walls. I know that for the modes, I have the standard Helmholtz Equation $$(\nabla^2+k^2)E_i=0$$ And I want the field to vanish at the walls. I solved it out just like a 3D 'Box', so that $$E(n_x,n_y,n_z)=\sqrt{\frac{8}{V}} \sin \left( \frac{n_x\pi x}{L} \right) \sin \left( \frac{n_y\pi y}{L} \right) \sin \left( \frac{n_z\pi z}{L} \right) .$$

This solves the equation, but I am not sure if this is what is wanted for solving for the modes. Thanks for pointing me in the right direction.

• What you have found are by definition the electric field profiles of the modes of the cavity. Good job! I note that the dimensions of your formula don't make sense though. $1/\sqrt{\text{volume}}$ is not electric field. – DanielSank Sep 17 '14 at 0:46
• If this is a homework problem, please add the homework tag and include a verbatim transcription of what the assignment says. Since you're asking whether or not your work satisfies the problem, we need to know what the problem is ;) – DanielSank Sep 17 '14 at 0:48
• So if I were to instead say that it was some constant E_0 and then normalize this equation, I should get something that makes a little more sense? – yankeefan11 Sep 17 '14 at 1:01
• Presumably to get the equation you have, you write down a guess for $E$ and then plug it into Poisson's equation or something like that. So, when you write down your guess, just make sure it has the right dimensions. Putting a constant $E_0$ out front is exactly the right thing to do. Once you work through Poisson's equation (or whatever) you'll wind up with an actual expression for $E_0$ in terms of parameters of the problem and natural constants. – DanielSank Sep 17 '14 at 3:29
• The electric field is a vector. Your general solution is a function. Are you sure about the boundary conditions for the electric field? – suresh Sep 17 '14 at 12:19