The Semi-Relativistic Equation Via the Shifted-l Expansion Technique

TL;DR

This paper introduces a method to solve the semi-relativistic equation with relativistic corrections using the shifted-l expansion technique, providing accurate eigenvalues for various potentials relevant in particle physics.

Contribution

The paper applies the shifted-l expansion technique to the semi-relativistic equation, offering a new approach to obtain eigenvalues with relativistic corrections for different potentials.

Findings

Accurate eigenvalues for Coulomb, Oscillator, and Coulomb-plus-linear potentials.

Method performs well across a wide range of r and quantum numbers.

Comparison with existing methods validates the approach.

Abstract

The semi-relativistic equation is cast into a second-order Schrodinger-like equation with the inclusion of relativistic corrections up to order (v/c)^2. The resulting equation is solved via the shifted-l expansion technique, which has been recently developed to get eigenvalues of relativistic and non-relativistic wave equations. The Coulomb, Oscillator, and the Coulomb-plus-linear potential used in qq-bar phenomenology are tested. The method gives quite accurate results over a wide range of r and any choice of quantum numbers n and l. However, a comparison of the present work with those of Lucha et al. and Nickisch et al. will serve as a test of this approach.