Rigorous inequalities in non-relativistic quantum mechanics with applications to quarkonium spectroscopy

The author shows that for a concave (convex) potential there are some inequalities for the ratios of the mass differences between excited anti qq states with different spin hold. Furthermore, if the confining potential generates spin forces by an admixture of solar and vector gluon exchanges, it is shown that the vector fraction must be less than 0.4. In this case some rigorous bounds are derived. The possibility of generating spin forces by scalar gluon exchange alone is also considered in some details. (HSI)