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When modelling spin in the Schrödinger equation, one has several alternatives which need to be chosen in advance. I'll copy an excerpt from a work of mine to give an overview (it considers atomic orbitals, but the idea is the same for a quantum well): For each alternative, the sought two-particle wavefunction would look like $$ \Psi(x_1,x_2) = \sum_{ij} c_{...

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