(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. 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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Identical particles and degenrate energy levels

**Physics Forums | Science Articles, Homework Help, Discussion**