show that the average energy eigenvalues of a free particle confined to a cube of length a are given by?

Question

h^2/8ma^2(nx^2+ny^2+nz^2)
nx,ny,nz=1,2,...

Answer 1

Since this sounds like a homework problem, I won't give the answer wholesale, but I'll give you a hint. A free particle confined to a cube is the 3D analog of the 1D particle in an infinite square well. The solution to Schroedinger's Eqn can be obtained by the method of separation of variables (http://en.wikipedia.org/wiki/Separation_of_variables#Partial_differential_equations). However, the big hint here was my second sentence.

Answer 2

Solve Born.