A simple method to construct eigenset of single-active-electron atom in momentum space with applications to solve time-dependent Schroedinger equation

We present a highly accurate method for solving single-active-electron (SAE) atomic eigenset in momentum space. The trouble of Coulomb kernel singularity is bypassed with numerical quadrature, which is simple but effective. The complicated Lande regularization method is no longer necessary. The data of accuracy for some low-lying states of the hydrogen and SAE helium atom were tabulated. Two examples of using the generated eigenset to solve the hydrogen atom under strong-field laser pulses were shown. The momentum and the coordinate representation are complementary to each other in quantum mechanics. The simple method to generate eigenstates and the localized behavior of wave functions in momentum space would be useful in the study of quantum mechanical problems involving continuous states.