Mass spectrum of Mesons via the WKB approximation method

TL;DR

This paper applies the WKB approximation to derive the mass spectra of mesons by solving the Schrödinger equation with a specific potential, showing good agreement with experimental data.

Contribution

It introduces a method to simplify multiple turning point problems in WKB to a single turning point case using Pekeris-type approximation for meson spectra analysis.

Findings

Energy eigenvalues match experimental data

Mass spectra are consistent with other analytical methods

Method effectively handles non-symmetric potentials

Abstract

In this paper, we demonstrated that the multiple turning point problems within the framework of the Wentzel-Kramers-Brillouin (WKB) approximation method can be reduced to two turning point one for a non-symmetric potential function by using an appropriate Pekeris-type approximation scheme. We solved the Schr\"odinger equation with the Killingbeck potential plus an inversely quadratic potential (KPIQP) function. The special cases of the modeled potential are discussed. We obtained the energy eigenvalues and the mass spectra of the heavy and heavy-light mesons systems. The results in this present work are in good agreement with the results obtained by other analytical methods and available experimental data in the literature