Symmetries and Conservation Laws — David J. Griffiths
Physics — Quantum Mechanics · spin_parity
Problem
Spin angular momentum, S^, is even under parity, just like orbital angular momentum L^:
Π^†S^Π^=S^or[Π^,S^]=0.(6.27)
Acting on a spinor written in the standard basis (Equation 4.139), the parity operator becomes a 2×2 matrix. Show that, due to Equation 6.27, this matrix must be a constant times the identity matrix. As such, the parity of a spinor isn't very interesting since both spin states are parity eigenstates with the same eigenvalue. We can arbitrarily choose that parity to be +1, so the parity operator has no effect on the spin portion of the wave function.