The time evolution of the ground state of the hydrogen atom in a very intense, linearly polarized, pulsed laser field is investigated by solving the two-dimensional Schroedinger equation. We use a unitary propagation scheme based on multiple application of the split operator formalism. For a realistic description, the Coulomb singularity is not cut off but treated exactly using fast sine transforms to switch between direct and Fourier space. The implementation and performance enhancement through parallelization on a Cray T3E are discussed.
Dehnen, R., & Großmann, F. (1999). Hydrogen wavefunction in intense laser fields: a unitary integrator for a high performance parallel computer. Computer Physics Communications, 120(1), 33–40. https://doi.org/10.1016/S0010-4655(99)00205-2