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## Homework Statement

Five electrons (with mass m) whose interaction can be neglected, are in the same 3-dim harmonic oscillatorpotential

[tex]V(x,y,z) = \frac k2 (x^2 + y^2 + z^2)[/tex]

What is the ground state energy?

## Homework Equations

## The Attempt at a Solution

I have the energy for the potential. It is:

[tex] E_{n_x,n_y,n_z} = (n_x+n_y+n_z + \frac 32)\frac{\hbar\omega}2[/tex]

My question is about the degeneracy.Since it's electrons, at most 2 of them can be in the same state, but can more than 2 electrons have the same energy?

Relating to this question: Should the ground state energy for this system be

[tex]E=2E_{111}+2E_{211}+E_{121}[/tex]

or are the two states (211) and (121) not allowed to have more than 2 electrons totally, ie

[tex]E=2E_{111}+2E_{211}+E_{221}[/tex]