Harmonic Potential of Non-Interacting Particles

[Lyons_63]

Two Non Interacting Particles Interact with a external harmonic Potential. What are the energy levels of the system, and the partition functions when assuming the particles are (b) Bosons and (c) Fermions

2. Homework Equations
Energy of the system
E=(ρ1)^2/2m + (ρ2)^2/2m+ mω^2/2 (x1+x2)

ρ= momentum
ω=angular frequency of the system


3. The Attempt at a Solution

The energy levels for a single oscillator are given by E=hbar ω (n + 1/2)
I am not sure to go from here and how to incorporate the fact that there are two particles in the system

Any help would be great!

 

[Redbelly98]

Since there are two particles, each will be found in one of the states n. So the state of the system would be characterized by two numbers rather than one -- you could call them n₁ and n₂. So first you'd need to write down the total energy of the system, when one particle is in state n₁ and the other is in state n₂.