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Jan
22
comment Wave functions for three identical fermions
It's too confusing to try to see how the L and S parts fit within the individual J ireps (to me at least). Same goes for trying to build things up with symmetrized and anti-symmetrized parts. Both these approaches do not scale to more complicated problems...
Jan
22
awarded  Teacher
Jan
22
comment Wave functions for three identical fermions
I don't think you can think of the j=5/2 state as being with L_{tot}=2, S_{tot}=1/2. An SU(2) irep is completely determined by a single label (here it's j). L and S are not necessarily conserved...
Jan
22
comment Wave functions for three identical fermions
I do not have these books so I can't comment on how they construct the basis for these ireps. In the past I saw many "add hoc" ways of combining symmetric and antisymmetric parts ...(for example in the construction of the proton spin 1/2 wavefunction from quarks with spin). What they have is probably ok, but choosing a basis always has more degrees of freedom than knowing how the space decomposes under the group.
Jan
22
answered Wave functions for three identical fermions