On the order of levels in charmonium

Abstract

We prove a theorem concerning the energies of the 2S and 3D states in a potential V(r) = −g 2 r + V c (r) , where V c is a non-singular confining potential. If ( d d r) 3(r 2V c ) is positive, then the 3D state lies above the 2S state, provided d dr 1 r d dr 2V c +r dV c dr < 0, ∀ r>0. For V c = r α , this corresponds to 0 < α < 2.