International Journal of

---

An approximate numerical method is proposed and discussed for solving the evolution of the spin density operator when the quantum system has an interaction with an external electromagnetic field. In this method by separating the relaxation and field interaction processes at small steps, instead of solving the conventional Liouville-von Neumann or Bloch differential equations, the time evolution of the density operator is efficiently obtained by a two-stage numerical algorithm. Here we have compared the results of this approach with Bloch equation results for a two-level quantum system. The proposed approach has potential applications in calculation of the time evolution for different atomic system including nuclear or electron spin resonance systems.