So I am in an introductory modern physics class and we discussed how intrinsic spin can be a linear combination of the spin basis. I am a bit confused on the physical representation of this and whether or not there are different basis to represent spin. If it is possible, what would be the point of doing so and how would you do it? From what I am understanding, spin can be treated like a coordinate system and you can use basic mathematical methods to represent spin in another coordinate system. Another question comes with the partial superposed spin states of an eigenstate. Doesn't the Pauli exclusion principle prevent this from happening?