A second mapping method in generalized discrete singular convolution algorithm: regularizing singularities for one electron system

A second mapping method is introduced in the generalized discrete singular convolution algorithm. The mapping approaches are adopted to regularize singularities for one electron system. The applications of the two mapping methods are generalized from the radial hydrogen problem to the one-dimensional hydrogen problem. Three mapping functions are chosen: the square-root mapping function, the cube-root mapping function, and the logarithm mapping function. However, the present mapping approaches fail in both the two-dimensional and three-dimensional hydrogen problems, because the wavefunctions of s-states at the nuclei are not correct.