1. Consider a pure ensemble of a spin 1/2 system.
Suppose , and the sign of are known.
Show how we may determine the state vector. Why is it unnecessary to know the magnitude of ?
2. Consider a mixed ensemble of a spin 1/2 system.
Suppose [Sx], [Sy] and [Sz] are known.
Show how we may construct the 2x2 density matrix which characterizes the ensemble.