Abstract
In this paper, we presented an approximate analytical treatment of the Coulomb plus logarithmic potential using time‐independent perturbation theory to investigate the mass spectra of bottomonium and charmonium mesons for the low‐order quantum states. Within the framework of the Schrödinger equation, we derived the energy equation to first‐order corrections and employed it to model the free potential parameters through fitting to experimental data of the Particle Data Group. The calculated bottomonium masses exhibited good agreement with experimental values, yielding an absolute percentage average deviation (APAD) of 0.25%, which improves upon previously reported theoretical results where the Pekeris type approximation was used to deform the centrifugal barrier and potential. Similarly, the vector and pseudoscalar charmonium masses were obtained with an APAD of 1.69%, demonstrating improved and comparable accuracy relative to existing competing theoretical calculations. Our results of the energy spectra to first‐order corrections in the absence of spin components gave small percent errors in comparison with exact numerical solutions obtained using the matrix Numerov method.