Quarkonia spectrum and wave functions with different trial basis in the potential model approach

Abstract

A numerical analysis based on the variational approach, using three different bases within a non-relativistic formalism, is performed to calculate the spectrum and wave functions of hydrogen atom and charmonium systems. Specifically, the Harmonic Oscillator, Generalized Harmonic Oscillator, and Gaussian bases are considered for this analysis. For the charmonium system, a non-relativistic kinetic energy is employed and the quark-antiquark interaction is represented by the Cornell potential plus the hyperfine interaction. The advantages of each basis are compared, with a focus on the spectrum and wave functions of the ground state and some excited states.