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October 16, 2025Open Access

Mass Spectrum of Heavy Mesons using WKB Approximation

BHB. J. HazarikaGauhati University TDTanmay DevGauhati University

Key Points

The quantization condition yields approximate energy levels of quarkonium systems, emphasizing essential dynamics.
Using the Cornell potential allows for accurate modeling of quark-antiquark interactions in bound states.
The semiclassical WKB approximation provides an efficient framework for simplifying the Schrödinger equation.
This method illustrates the potential for analytical treatments within quantum mechanics, enhancing future studies.

Abstract

In this study, we analyze the bound-state energy spectrum of quark-antiquark systems using the semiclassical WKB approximation. We consider the Cornell potential, which combines a linear confinement term with a Coulombic interaction, and perform a Taylor series expansion around an appropriately chosen point r₀ to simplify the potential near the classical turning points. This expansion enables an analytic treatment of the Schrödinger equation within the leading-order WKB framework. The resulting quantization condition yields approximate energy levels that capture the essential dynamics of quarkonium systems and illustrate the utility of the WKB method in modeling hadronic bound states.

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