Bound state solution of the Schrödinger equation at finite temperature

In this article, the bound state solution of the modified radial Schrodinger equation is obtained for the sum of Cornell and inverse quadratic potential. Here in, the developed scheme is used to overcome the centrifugal part at the finite temperature and the energy eigenvalues and corresponding radial wave functions are defined for any angular momentum case via the Nikiforov-Uvarov methods. The present result are applied on the charmonium and bottomonuim masses at finite and zero temperature. Our result are in goog agreement with other theoretical and experimental results. The zero temperature limit of the energy spectrum and eigenfunctions is also founded. It is shown that the present approach can successfully be apply to the quarkonium systems at the finite temperature as well. (paper)