We show how a large class of sufficient conditions for the existence of bound
states, in non-positive central potentials, can be constructed. These
sufficient conditions yield upper limits on the critical value,
gc(ℓ)​, of the coupling constant (strength), g, of the
potential, V(r)=−gv(r), for which a first ℓ-wave bound state appears.
These upper limits are significantly more stringent than hitherto known
results.Comment: 7 page