1. The problem statement, all variables and given/known data An #a*b*c box is given in x,y,z (so it's length #a along the x axis, etc.). Every face is kept at #V=0 except for the face at #x=a , which is kept at #V(a,y,z)=V_o*sin(pi*y/b)*sin(pi*z/c). We are to, "solve for all possible configurations of the box's potential" 2. Relevant equations Differential equation solutions (Method of assuming V(x,y,z) = X(x)Y(y)Z(z) and then solving for each. #X''/X + Y''/Y + Z''/Z = 0 --> X'' - (Cx)*X = 0, etc. Cx+Cy+Cz=0 (same as the first) 3. The attempt at a solution I first tried to limit how many possible XYZ configurations I had to check. Because V(a,y,z) is in the form of sines of y and z, I thought I could safely choose Y, Z to be of trigonometric form (i.e. the constants they equal are negative). However if they are both of this form, then X is confined to only be of exponential solutions form (because the three constants need to add to zero) which means "all possible configurations" would only be one configuration. I tried looking at other forms but there are so many I feel as though I must be missing some key point to eliminate all but a few (i.e. "Oh, well actually you can still have a f(sin(z)) solution even if Z is linear!". I believe I can successfully solve for the Fourier coefficients and ultimately the solution(s), but I'm stuck on the boundary conditions for now.