Bound State Solution Schr\"{o}dinger Equation for Extended Cornell Potential at Finite Temperature

TL;DR

This study analytically solves the finite temperature Schr"odinger equation with an extended Cornell potential, providing insights into heavy quarkonia and meson masses and their temperature dependence.

Contribution

It introduces an analytical approach using the Nikiforov-Uvarov method to solve the temperature-dependent Schr"odinger equation with an extended potential.

Findings

Energy eigenvalues and wave functions derived analytically.

Mass predictions for heavy quarkonia and B_c mesons match experimental data.

Temperature effects vary with quantum numbers and align with QCD sum rule results.

Abstract

In this paper, we study the finite temperature-dependent Schr\"{o}dinger equation by using the Nikiforov-Uvarov method. We consider the sum of the Cornell, inverse quadratic, and harmonic-type potential as the potential part of the radial Schr\"{o}dinger equation. Analytical expressions for the energy eigenvalues and the radial wave function are presented. Application of the results for the heavy quarkonia and $B_c$ meson masses are good agreement with the current experimental data except for zero angular momentum quantum numbers. Numerical results for the temperature dependence indicates a different behaviour for different quantum numbers. Temperature-dependent results are in agreement with some QCD sum rule results from the ground states.