# Particle in a 3D box

charbon

## Homework Statement

For a system consiting of a single particle of mass m in a box of volume L^3 (Lx = Ly = Lz = L) develop a relation between the number of accessible states, Ω(E) and E

## Homework Equations

E = ((π^2ћ^2)/(2mL^2))(nx^2 +ny2 +nz2)

## The Attempt at a Solution

nx^2 + ny^2 + nz^2 = (2mEL^2)/(π^2ћ^2)

this is the equation of a sphere. The next step would be to find the number of states with energy inferior to E (ψ(E)) but I'm a bit clueless about how to do that with the equation. Could someone clarify that for me? Thanks in advance

If you can assume that the radius of the sphere is much larger than 1, you can use a volume integral to approximate the sum over states. You must be careful that your counting respects that the $$n_i>0$$.