Unlike regular wavefunctions, spin wavefunctions do not exist in real space. Likewise, the spin angular momentum operators cannot be represented as differential operators in real space. Instead, we ne...Unlike regular wavefunctions, spin wavefunctions do not exist in real space. Likewise, the spin angular momentum operators cannot be represented as differential operators in real space. Instead, we need to think of spin wavefunctions as existing in an abstract (complex) vector space. The different members of this space correspond to the different internal configurations of the particle under investigation. Note that only the directions of our vectors have any physical significance.
