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Harmonic Potential of Non-Interacting Particles

  1. Mar 15, 2012 #1
    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. Relevant 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!
     
  2. jcsd
  3. Mar 18, 2012 #2

    Redbelly98

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    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.
     
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