Precise integration for the time-dependent Schroedinger equation

The precise integration method proposed for linear-invariant dynamical system can give precise numerical result approaching to the exact solution at the integration points. In this paper, a cheap and easy to implement precise integration method for time-dependent Schroedinger equation with periodic Hamiltonians is presented based on Magnus expansion of the solution of the system. The method requires evaluation of only one exponential of matrix, and preserves many of the qualitative properties of the exact solution