The most general state operator for a spin 1/2 system has the form given in Eq. (7.50), = 1/2(1 + a), where a is a vector whose length is not greater than 1. If the system has a magnetic moment = 1/2 and is in a constant magnetic field B, calculate the time-dependent state operator (t) in the Schrodinger picture. Describe the result geometrically in terms of the variation of the vector a.