Abstract

• In the constituent quark model, charmonium and bottomonium are considered to be the bound states of charm/anti-charm and bottom/antibottom quarks. We use the linear potential to represent the long distance confining part of the potential and a Coulomb like potential to represent the short distance one-gluon exchange part of the potential. In order to study the general features of the wave functions, it is not necessary to include spin dependent parts in the potential. Using the above mentioned potentials, we solved the Schrodinger equation with non-relativistic kinematics and also with relativistic kinematics. We solve these equations by expanding the momentum space wavefunction in a complete set of orthonormal basis functions and turning the Schrodinger equation into a standard matrix eigen-value equation. We vary the masses of the quarks, and the strengths of the potentials until we get a satisfactory fit to the spin averaged mass spectra of the desired ??̅ system. The eigenvectors gives the coefficients of the linear combination in the wavefunction expansion from which we can construct the wavefunctions. We compare the non- relativistic and relativistic wavefunctions for each state in ??̅ and ??̅ systems.