meegal90 wrote:Is the answer is 3 fold degenerate with nx,ny and nz values 1,1,3 respectively??
No, and, err..no. So the idea of degeneracy is to count the number of possible combinations of quantum numbers that gives the appropriate energy, with the rule that the n's are quantized as integers. So saying that nx = ny = 1, and nz = 3 is the answer isn't right--that could be one of the ways, but certainly not all; if that's allowed, so is nx = nz = 1, and ny = 3.
Also, you're in a 2-D well, so there are only 2 quantum numbers, not 3 (which is fortunate, because otherwise this particular energy state would be impossible). Wikipedia states E = (hk)^2/(8mPi^2), with k^2 = k(dot)k = pi^2/a^2(nx^2+ny^2).
http://en.wikipedia.org/wiki/Particle_in_a_box#Higher-dimensional_boxesSo, that should be enough to answer the question, which is really how many ways can you have nx^2 + ny^2 = 25, since everything else is just a constant, the same on both sides, which allows you to cancel.