Computation of Energy Eigenvalues of the Anharmonic Coulombic Potential with Irregular Singularities

TL;DR

This paper presents a highly efficient and accurate numerical method combining Sinc collocation and double exponential transformation to compute energy eigenvalues of anharmonic Coulombic potentials with irregular singularities in the Schrödinger equation.

Contribution

It introduces a novel numerical approach that improves the accuracy and efficiency of eigenvalue computations for complex quantum potentials.

Findings

Method achieves high accuracy in eigenvalue computation

Demonstrates efficiency on irregular singularities

Codes are openly available in Julia

Abstract

The present contribution concerns the computation of energy eigenvalues of a perturbed anharmonic coulombic potential with irregular singularities using a combination of the Sinc collocation method and the double exponential transformation. This method provides a highly efficient and accurate algorithm to compute the energy eigenvalues of one-dimensional time-independent Schr\"odinger equation. The numerical results obtained illustrate clearly the highly efficiency and accuracy of the proposed method. All our codes are written in Julia and are available on github at \url{https://github.com/pjgaudre/DESincEig.jl}.