J-Matrix time propagation of atomic hydrogen in attosecond fields

The J-Matrix approach for scattering is extended to the time-dependent Schrödinger equation (TDSE) for one electron atoms in external few cycle attosecond fields. To this purpose, the wave function is expanded in square integrable ([Formula: see text] ) Sturmian functions and an equation system for the transition amplitudes is established. Outside the interaction zone, boundary conditions are imposed at the border in the [Formula: see text] function space. These boundary conditions correspond to outgoing waves (Siegert states) and minimize reflections at the [Formula: see text] boundary grid. Outgoing wave behaviour in the asymptotic region is achieved by employing Pollaczek functions. The method enables the treatment of light - atom interactions within arbitrary external fields. Using a partial wave decomposition, the coupled differential equation system is solved by a Runge-Kutta method. As a proof of the method ionization processes of atomic hydrogen in half and few cycle attosecond fields are examined. The electron energy spectrum is calculated and the numerical implementation will be presented. Different forms of the interaction operator are considered and the convergence behaviour is discussed. Results are compared to other studies which use independent approaches like finite difference methods. Remarkable agreement is achieved even with strong field strengths of the electromagnetic field. It is demonstrated that expanding in [Formula: see text] functions and imposing boundary conditions at the limit in the [Formula: see text] function space can be an advantageous alternative to conventional propagation methods using complex absorbing potentials or complex scaling.