In this study, a non-relativistic two-body wave equation is used to describe the properties of heavy quark–antiquark systems with a potential proportional to the ψ-function. The wave equation is transformed into a true eigenvalue equation and solved numerically. Both the resonance masses and the leptonic decay widths of cc and bb mesons are calculated. The obtained results showed that the quark–antiquark interaction in these systems could be described adequately by using this simple potential form.