Calculation of atomic hydrogen and its photoelectron spectra in momentum space

An essential modification to the kernel in the numerical calculation of hydrogenic momentum wave functions, is presented in this paper. Using only 256 grid points, the calculated eigenvalues, eigenfunctions and the oscillator strengths are shown to be in excellent agreement with the exact analytic results. The reliable pseudocomplete set of momentum space eigenfunctions is then applied to the time-dependent calculation of intense laser pulse on the hydrogen atom. With the advantage of having no boundary reflection during the time evolution, like that inherent in the coordinate space method, the photoelectron spectra of above-threshold-ionization (ATI) are elucidated for four cases. Some of which are not feasible or very difficult to solve with the coordinate space method. Generalization of the method to single-active electron systems is straightforward. Due to the good accuracy with a reasonably small-sized basis set, applications to the currently interested intense case of laser pulse on atom or molecule are expected.