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

TL;DR

This paper introduces a simple, accurate method for constructing the eigenset of single-active-electron atoms in momentum space, facilitating solutions to the time-dependent Schrödinger equation without complex regularization.

Contribution

The method bypasses Coulomb kernel singularity using numerical quadrature, eliminating the need for Lande regularization, and provides accurate eigenstates for hydrogen and helium atoms.

Findings

Accurate eigenstates for hydrogen and helium atoms were tabulated.

The method effectively solves the TDSE for atoms in strong laser fields.

Momentum and coordinate representations are shown to be complementary.

Abstract

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.