a) Compute the above matrix elements Kr1, r2, f, mziki, k2 , t , m’z) for all four of the spin basis states It, mz). You will have to take into account that the total wavefunction must be antisymmetric under the exchange of the two particles.
b) Using your results from (a), compute the density matrix Kr1, r2, f, nizIP2Iri, r2, f, mz) for all four of the spin basis states It, mi).
You should find that for any of the spin triplet states, the density matrix has the same dependence on Iri – r21 as we found previously for two spinless fermions, i.e. there is an effective repulsion at small separations.
However for the spin singlet state, the density matrix has the same dependence on Iri – r21 as we found previously for two spinless bosons, i.e. there is an effective attraction at small separations. Give a simple physical argument as to why this is a reasonable result.
This is the origin of Hund’s rule of atomic physics. As one fills up a partially full e
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