Compact schemes for laser-matter interaction in Schr\"odinger equation

Numerical solutions for laser-matter interaction in Schr"odinger equation has many applications in theoretical chemistry, quantum physics and condensed matter physics. In this paper we introduce a methodology which allows, with a small cost, to extend any fourth-order scheme for Schr"odinger equation with time-indepedent potential to a fourth-order method for Schr"odinger equation with laser potential. These fourth-order methods improve upon many leading schemes of order six due to their low costs and small error constants.