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

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