Particle in a 3D box (Quantum)

[breeg]

Homework Statement

What are the degeneracies of the first four energy levels for a particle in a 3D box with a=b=1.5c?

Homework Equations

E_xxnynz=h²/8m(n_x²/a²+n_y²/b²+n_z²/c²)

For 1st level, the above = 3h²/8m
For 2nd level, the above = 6h²/8m
For 3rd level, the above = 9h²/8m
For 4th level, the above = 11h²/8m

The Attempt at a Solution

I think I finally grasped the basis of what the problem wants.

For the 1st level:

E_xxnynz=(h²/(8m*1) + h²/(8m*1) + h²/8m*(1/1.5))*(1+1+(3/2))

So E_{1 1 3/2}

3/2 was obtained because 1/1.5 is 2/3=c because a=b=1=1.5c so c=1/1.5=2/3

Is this correct? I'm just unsure about the rest of the energy levels. It seems like one can just pick numbers and force it to work so I'm lost on the proper degeneracy.

 

[BruceW]

For the 1st level:

E_xxnynz=(h²/(8m*1) + h²/(8m*1) + h²/8m*(1/1.5))*(1+1+(3/2))

Why are you multiplying by (1+1+3/2)? I don't think you've got the idea. The quantum numbers each take on an integer value, and that is why the energy levels are different.