  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.
