CCAST, World Lab, Beijing 100080, Peoples R China
; Acad Sinica, Grad Sch, Dept Phys, Beijing 100039, Peoples R China
; Nankai Univ, Dept Phys, Tianjin 300071, Peoples R China
; Acad Sinica, Inst High Energy Phys, Beijing 100039, Peoples R China
; Univ Milan, Dept Phys, I-20133 Milan, Italy
We carefully study the energy eigen-values and splitting of heavy quarkonia as there exist l/r(3) and delta(3)((r) over right arrow) singular terms in the potential which make a direct numerical solution of the Schrodinger equation impossible. We compare the results obtained in terms of perturbation and variational methods with various treatments.