Killingbeck Mass Spectrum of Heavy Quarkonia Under the Influence of External Magnetic and AB Flux Fields

TL;DR

This paper derives a generalized Schrödinger equation in curvilinear space to analyze the mass spectrum of heavy quarkonia under external magnetic and Aharonov-Bohm flux fields, including thermodynamic properties.

Contribution

It introduces a novel approach using curvilinear coordinates to solve the Schrödinger equation with Cornell plus harmonic potentials under external fields for heavy quarkonia.

Findings

Calculated energy spectra for charmonium and bottomonium

Analyzed thermodynamic functions under external fields

Explored effects of potential parameters, magnetic field, and temperature

Abstract

We present a more general form of the Schr\"odinger equation in curvilinear space that is exposed to external fields. Thereby, we solve the wave equation with the Cornell plus harmonic potentials (CHP) under the influence of the magnetic and Aharonov-Bohm (AB) flux fields using curvilinear coordinates system in such space. With this requirement, the energy spectrum and the corresponding wave functions are calculated by means of the series method. The mass spectrum of both charmonium and bottomonium states consisting of quark and antiquark are calculated. In addition, the main thermodynamic functions such as the free energy, the mean energy, the entropy, the specific heat, the persistent currents and magnetization are obtained by using the characteristic function. We draw the resulting energy states and the thermodynamic quantities versus some potential parameters, magnetic field and temperature to see their numerical behaviors. Finally, we give some discussions to our results.