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Two distinguishable particles in a box.

  1. Feb 21, 2014 #1
    Hi,
    1. The problem statement, all variables and given/known data
    I would like to determine the number of energy states two free, distinguishable particles in a box of length L have. I would then like to determine the number of states two free, indistinguishable particles, with spin 3/2 each, have in that box at the elementary level. Finally, determine the number of states in case these two particles with spin 3/2 each are distinguishable.


    2. Relevant equations



    3. The attempt at a solution
    I am familiar with the following formula for the energy states
    En=(hbar)2π2n2/(2mL2)
    but am not sure how to proceed. If the particles are distinguishable, does that entail that one is a fermion whereas the other is a boson? I am not sure.
    Furthermore, if the two particles have spin 3/2 each, that means they are both fermions, right? If that is correct, then, due to Pauli's exclusion principle, the two could not be at the same state. I also know that for spin 3/2 there could be 4 particles per energy level. But again I am not sure how to coherently process the given data and would appreciate some guidance.
     
  2. jcsd
  3. Feb 21, 2014 #2
    In case the spin of each particle is 3/2, would the number of energy states be 4!/(2!2!) for indistinguishable particles and 4!2! for distinguishable particles? (at the elementary level)
     
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