Accurate and efficient trigonometric discrete variable representations for the singular Coulomb potential

Abstract A trigonometric discrete variable representation with two well-designed scaling functions (mapping functions) was introduced for solving the Schrödinger equation with the singular Coulomb potential, which have distinctly different distributions of the grid points. The method has surprisingly rapid convergence, even faster than the best available (pseudo-)spectral methods. Since the fast Fourier transformation technique could be directly adopted with this method, it is expected to be of a wide range of applications for solving the Schrödinger equation of the electronic motion in atoms, such as the attosecond physical processes. The findings of the work also revealed the marvelous convergence behaviors of the (pseudo-)spectral methods for the singular Coulomb potential.