Upper limit on the number of bound states of the spinless Salpeter equation

We obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of l-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the ultrarelativistic case (m=0), for the existence of at least one l-wave bound states: C(l,p/(p-1))∫0∞dr rp-1 vertical bar V-(r) vertical bar p≥1, where C(l,p/(p-1)) is a known function of l and p>1