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Homework Help: Show that the total eigenfunction must be antisymmetric

  1. Apr 20, 2017 #1
    1. The problem statement, all variables and given/known data

    By considering the eigenfunctions for 2 noninteracting particles at distances r1 and r2,
    show that their total eigenfunction must be antisymmetric.
    2. Relevant equations

    Spatial wavefunctions:

    Ψ(x1,x2) = 1/√2 [ ψA(x1B(x2) ± ψA(x2B(x1)]

    Where + gives a symmetric wavefunction and - gives an antisymmetric one.

    3. The attempt at a solution

    Hi, not really sure what to do with this one. I know that the Pauli exclusion principle says that the total eigenfunction must be antisymmetric for fermions. But the question doesn't mention fermions, just "2 noninteracting particles". I also know that the antisymmetric spin wavefunctions are associated with the symmetric spatial wavefunctions, and vice versa, to produce a total antisymmetric wavefunction, but I don't get why, which is what the question seems to be asking...

  2. jcsd
  3. Apr 21, 2017 #2


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    Staff: Mentor

    The question is very poorly worded. The wave function is anti-symmetric with respect to what? Bad questions have no good answers :frown:
  4. Apr 21, 2017 #3
    Hi, sorry, I should probably have said a bit more in my OP. Presumably, in the question, the 2 particles are indistinguishable. So it means that eigenfunction must be antisymmetric under particle exchange. ie. that if the particles are swapped, this will give the negative of the original eigenfunction
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