On the bound states of spin-1/2 particles for certain central potentials

Bound state solutions of the Dirac equation for spin 1/2 particles are investigated by the polynomial method for potentials V(r) where rV(r) = lambdasub(0)+lambdasub(1)r+lambdasub(2)r2+....., O<r<infinity, V(r)→0 as r→ infinity. It is deduced that except for a special class of potentials satisfying restrictive conditions, bound states do not exist and that the necessary condition for a potential V(r) to define bound state solutions is that Λsub(i) should satisfy certain equalities which are stated. (K.B.)