Solving time-dependent Schrodinger equation in momentum space with application to strong-field problems

We present a numerical method to solve the time-dependent Schrodinger equation (TDSE) in momentum representation (p-space). We show that the method is practically useful and easier than the coordinate space (r-space) method when continuous states are involved. For a single-active electron (SAE) atom, the numerically complete eigenset can be accurately constructed in p-space by quadrature method which bypasses the singularities in the Coulombic kernel. Although there is an ingenious Lande subtraction for dealing with the singularity but is not straightforward. We formulate the time marching algorithms for an SAE atom in linearly polarized (LP) laser pulse and in circularly polarized (CP) pulse, respectively. We show calibrations to literature results to justify the formulations. Argon in a resonant and a nonresonant CP pulse are investigated and show distinct properties from the case of tunneling regime. Together with the currently available powerful graphics processing unit (GPU) for massively parallel computing, the p-space method could provide a useful alternative tool for some problems such as atoms in intense light pulses.