The exact solution of Schr?dinger equation for two spin-1/2 particles under the rotating magnetic field is obtained. It is proposed that pulse bandwidth is a crucial factor in population transfer. The figures of energy and population are analysed, and the results show that bandwidth of pulse decides if there is an exchange between states at the places of energy degeneracy. Comparing our result with Unanyan’s, it is found that whether the adiabatic condition is satisfied exactly or not is not important, and the adiabatic condition that they derived may not be a reliable criterion for preparing entangled states.