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Mattofix

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## Homework Statement

What is the chemical potential, [tex]\mu[/tex] (in units of [tex]\hbar\omega[/tex]) at T = 0 K of 44 [tex]^{6}Li[/tex] atoms with spin 1/2 contained in a 3D harmonic potential well (energy levels, [tex]\epsilon_{i}=(i+3/2)\hbar\omega[/tex] with degeneracies [tex]g_{i}= 1/2(i+1)(i+2)[/tex] )?

## Homework Equations

## The Attempt at a Solution

spin = 1/2 [tex]\Rightarrow[/tex] Fermoins

t=0 [tex]\Rightarrow[/tex] [tex]\mu=\epsilon_{f}[/tex] (fermi energy)

therefore:

So i need 'i' to then use in [tex]\epsilon_{i}=(i+3/2)\hbar\omega[/tex] to obtain [tex]\mu[/tex].

I know that [tex]\frac{n_{i}}{g{i}} = 1/2[/tex] and that [tex]g_{i}= 1/2(i+1)(i+2)[/tex] so all i need is the value of [tex]n_{i}[/tex], which is the number of particles in each [tex]g_{i}[/tex].

Is this all correct? If how do i obatin [tex]n_{i}[/tex]?