Simple, accurate, and efficient implementation of 1 electron atomic time dependent Schrodinger equation in spherical coordinates
Modelling atomic processes in intense laser fields often relies on solving the time dependent Schrodinger equation (TDSE) For processes involving ionisation, such as above threshold ionisation (ATI) and high harmonic generation (HHG) this is a formidable task even if only one electron is active. Several powerful ideas for efficient implementation of atomic TDSE were introduced by H.G. Muller some time ago (Muller, 1999) including: separation of Hamiltonian terms into tri diagonal parts; implicit representation of the spatial derivatives; and use of a rotating reference frame. Here, we extend these techniques to allow for non uniform radial grids, arbitrary laser field polarisation, and non Hermitian terms in the Hamiltonian due to the implicit form of the derivatives (previously neglected) We implement the resulting propagator in a parallel Fortran program, adapted for multi core execution. Cost of TDSE propagation scales linearly with the problem size, enabling full dimensional calculations of strong field ATI and HHG spectra for arbitrary field polarisations on a standard desktop PC.
Comput. Phys. Commun.