Analytic solution of multi-dimensional Schrödinger equation in hot and dense QCD media using the SUSYQM method

Abstract

The N-radial Schrodinger equation is analytically solved by using the SUSYQM method, in which the heavy-quarkonia potential is introduced at finite temperature and baryon chemical potential. The energy eigenvalue is calculated in the N-dimensional space. The obtained results show that the binding energy strongly decreases with increasing temperature and is slightly sensitive for changing baryon chemical potential up to 0.6GeV at higher values of temperatures. We employed the nonperturbative corrections to the leading-order of the Debye mass at finite baryon chemical potential. We found that the binding energy is more dissociated when the nonperturbative corrections are included with the leading-order term of the Debye mass in both hot and dense media. A comparison with other works, such as the lattice parameterized of the Debye mass is discussed; thus, the present potential with the SUSYQM method provides satisfying results for the description of the dissociation of binding energy for heavy quarkonia in hot and dense media.