The evolution of spin 1/2 particles in a rotating magnetic field is discussed. Then the wavefunction of the spin 1/2 particles by using the method of rotating frame is also obtained. At last, the spin reversal ratio, spin polarization vector and non-adiabatic geometric phase in case of resonance and non-resonance are calculated.
The geometric phase for states of two spin-1/2 particles in rotating magnetic field is calculated, in particular, the noncyclic and cyclic non-adiabatic phases for the general case are explicitly derived and discussed. We find that the cyclic geometric phase for the entangled state can always be written as a sum of the phases of the two particles respectively; the same cannot be said for the noncyclic phase. We also investigate the geometric phase of mixed state of one particle in a biparticle system, and we find that the geometric phase for one subsystem of an entangled system is always affected by another subsystem of the entangled system.