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

TL;DR

This paper introduces a second mapping method in the generalized discrete singular convolution algorithm to regularize singularities in one-electron systems, extending from radial to one-dimensional hydrogen problems, but it faces limitations in higher dimensions.

Contribution

The paper proposes a new mapping approach within the generalized discrete singular convolution algorithm specifically for one-electron systems, exploring different mapping functions.

Findings

Effective in one-dimensional hydrogen problems

Fails in two- and three-dimensional hydrogen problems

Wavefunctions at nuclei are not accurately represented in higher dimensions

Abstract

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.