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Assume I’m solving a 2-particle (fermions) problem in a potential well. If I set the wavefunction as anti-symmetric, then by default I’m assuming that the two particles has the same spin and hence exchange interaction has to be accommodated for.

But what if the 2 fermions have different spins? Shouldn't in this case I set the wavefunction to be only symmetric (since no Pauli exclusion here)? And what would be the final wave function? Is it a normalized linear combination of the 4 cases (2 ups, 2 downs, and 2 mixed-spin)?

Thanks for your help on that.

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# Spin assumption for fermions in potential well.

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