Abstract: Methods and systems for calculating electron or ion dynamics using spin-dependent quantum trajectories are disclosed. According to one exemplary embodiment of the present invention, electron or ion dynamics are obtained by solving a set of equations for electrons' motion using spin-dependent quantum trajectories calculated from electron current with one equation for each electron in the atomic structure of a material of interest. The set of equations is time-dependent Schrödinger or Dirac equations for the nonrelativistic and relativistic regime, respectively. The electron current contains a set of spin-dependent terms that guarantee Fermi-Dirac statistics are obeyed. Steady state solution of the set of equations for electrons' motion is a set of wave functions in a three-dimensional space and in time. The spin-dependent quantum trajectories for each of the electrons are updated at each solution cycle, and therefore, mean-field approximation is avoided.