Homework Help: N spin 1/2 particles in 3D harmonic oscillator potential

1. Dec 16, 2012

darthmonkey

1. The problem statement, all variables and given/known data
The 3-dimensional harmonic oscillator potential holds N identical non-reacting spin 1/2 particles

a)How many particles are needed to fill the low lying states through E=(3+3/2)$\bar{h}$ω

b)What is the total energy of the system

c)what is the fermi energy

2. Relevant equations
E=(n+3/2)$\bar{h}$ω
n=nx+ny+nz=3

3. The attempt at a solution
a)(1,0,0)*3,(1,1,0)*3,(2,0,0)*3,(1,1,1),(2,1,0)*6,(3,0,0)*3
19 states for 38 total particles
b)6E1+12E2+20E3=147$\bar{h}$ω
c)Ef=(3+3/2)$\bar{h}$ω
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So I'm pretty sure I did part a correct. If so part b should just be the sum of the number of particles at each energy right?

For part c isn't the given energy the fermi energy since I'm finding all the states below it?

I'm not really sure about my reasoning on the part b and c