E = (h^2)/(8mL^2)*[(n_x)^2 + (n_y)^2 + (n_z)^2)
where L is the length of one side of the cube, m is the mass of the particle, and the n's are independent integers that can take any value from 1 and up,
n_x = 1,2,3,4,K
n_y = 1,2,3,4,K
n_z = 1,2,3,4,K
In other words, the individual n's determine the microstates.
If the total energy is E = (h^2)/(8mL^2)(12) what is the multiplicity of that state?
First, you have to realize that because the two particles are symmetrical, there are a lot of equivalent states ie. for particle 1, P1(nx, ny, nz) we can have P1(1, 2, 1) and it will be equal to P1(2, 1, ...
We have to solve P1(nx, ny, nz) + P2(nx, ny, nz) = 12.