  We derive rigorously the reduced dynamical law for quantized vortex dynamics
of the nonlinear Schr\"odinger equation with wave operator on the torus when
the core size of vortex $\varepsilon \to 0$. It is proved that the reduced
dynamical law of the nonlinear Schr\"odinger equation with wave operator is a
mixed state of the vortex motion laws for the nonlinear wave equation and the
nonlinear Schr\"odinger equation. We will also investigate the convergence of
the reduced dynamical law of the nonlinear Schr\"odinger equation with wave
operator to the vortex motion law of the nonlinear Schr\"odinger equation via
numerical simulation.
