en عمومى General پژوهشي Research 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. Bloch equation, Liouville-von Neumann equation, Two level quantum systems, Spin density operator dynamics. 169 176 http://ijop.ir/browse.php?a_code=A-10-655-2&slc_lang=en&sid=1 Maryam Hatefi maryam.hatefi@ut.ac.ir 10031947532846003479 10031947532846003479 No Magnetic Resonance Research Laboratory, Department of Physics, College of Science, University of Tehran, 143-9955961, Tehran, Iran. Farrokh Sarreshtedari f.sarreshtedari@ut.ac.ir 10031947532846003480 10031947532846003480 Yes Magnetic Resonance Research Laboratory, Department of Physics, College of Science, University of Tehran, 143-9955961, Tehran, Iran. Mahmood Sabooni saboonim@gmail.com 10031947532846003481 10031947532846003481 No Department of Physics, College of Science, University of Tehran, 143-9955961, Tehran, Iran. Institute for Quantum Computing, Department of Physics and Astronomy, Waterloo, Ontario, N2L3G1, Canada.