Variational and exact solutions of the wavefunction at origin (WFO) for heavy quarkonium by using a global potential

In this paper, we discuss the wavefunction at origin (WFO) for b (b) over bar, c (c) over bar and b (c) over bar massive quarks systems. Using the variational method and an exact computation of the Schrodinger equation, we computed the WFO and also expectation values of < 1/r >, < r > for massive mesons, while we had global potential in the form of V(r) = k(root r + alpha/r). We show that the final results of this potential include and cover all other results by other potential models (Cornell, Martin, logarithmic, Lichtenberg, etc). Also, the energy values obtained from this model have the highest level compared with other models.