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Wavefunction of 2 electron system

  1. Feb 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Ignoring the repulsion force between two electrons, one of the electrons is in 1s state and the other is in 2p state. what is the total wavefunction of the system that is made up of the multiplication of the spatial wavefunctions and spin values?

    2. Relevant equations

    so, if electron(1) is in 1s state and e(2) is in 2p state, their spatial wavefunction will be :
    u1(r1)u2(r2) - u1(r2)u2(r1)
    with spins of
    chi-(1) chi+2 and so on



    3. The attempt at a solution

    there are 8 possible products of spatial wavefcn and their spins for both electrons individually, I think there are only 4 combinations that are allowed by exclusion principle, those are:

    {u1(r1)u2(r2) - u1(r2)u2(r1) }χ+(1) χ+(2)

    {u1(r1)u2(r2) - u1(r2)u2(r1) }χ-(1) χ-(2)

    u1(r1)u2(r2) {χ-(1) χ+(2) } - u1(r2)u2(r1) {χ-(2) χ+(1) }

    u1(r1)u2(r2) {χ-(2) χ+(1) } - u1(r2)u2(r1) {χ-(1) χ+(2) }

    Im not sure if the last combination is necessary, it kinda looks like the third one, any ideas? does the whole combination makes sense?

    Thanks
     
  2. jcsd
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