<title>On the Kantorovich approach for calculations of the hydrogen atom states affected by a train of short pulses</title>

Abstract

We present theoretical calculations for the evolution of Zeeman states in a train of short electric half-cycle pulses (kicks). For the numerical solution of the corresponding time-dependent Schrodinger equation (TDSE) the high accuracy splitting scheme based on the unitary approximations of the evolution operator is developed. The finite element method is used for determining the spatial form of the solution. The efficiency and stability of the developed computational method is shown for 1D models in the cases of second-, forth-, and sixth-order accuracy with respect to the time step. Numerical calculations for the kicked hydrogen atom in the presence of magnetic field are performed using the scheme of the sixth-order accuracy with respect to a time step and both Galerkin and Kantorovich reductions of the problem with respect to the angular variables. For a particular choice of the electric- and magnetic-field parameters and the initial Zeeman state the corresponding results exhibit a two-state resonance picture.