To add: I think the other use of “pure state” comes from this context. Here if you have a system of commuting operators and take a joint eigenspace, the projector is mixed, but it is pure if the joint eigenvalue uniquely determines a 1D subspace; and then I think this terminology gets used for wave functions as well
To add: I think the other use of “pure state” comes from this context. Here if you have a system of commuting operators and take a joint eigenspace, the projector is mixed, but it is pure if the joint eigenvalue uniquely determines a 1D subspace; and then I think this terminology gets used for wave functions as well