High-precision methods for Coulomb, linear confinement and Cornell potentials in momentum space

TL;DR

This paper introduces high-precision numerical methods for solving the Schrödinger equation in momentum space with Coulomb, linear confinement, and Cornell potentials, achieving superior accuracy over existing techniques.

Contribution

The authors develop special quadrature formulas for singular integrals to accurately compute eigenvalues in momentum space for various potentials, including zero angular momentum states.

Findings

Eigenvalues calculated with high accuracy surpass other methods

Effective solution techniques for zero angular momentum states

Demonstrated superiority of the methods in numerical precision

Abstract

We use special quadrature formulas for singular and hypersingular integral to numerically solve the Schr\"{o}dinger equation in momentum space with the linear confinement potential, Coulomb and Cornell potentials. It is shown that the eigenvalues of the equation can be calculated with high accuracy, far exceeding other calculation methods. Special methods of solution for states with zero orbital angular momentum are considered.