UPPER LIMITS FOR THE NUMBER OF BOUND-STATES ASSOCIATED WITH THE YUKAWA POTENTIAL

The number of bound-state solutions of the Schroedinger equation for the screened Coulomb potential (Yukawa potential), -(C/r) exp( minus alpha r), occurs frequently in theoretical discussions concerning, for example, gas discharges, nuclear physics, and semiconductor physics. The number of bound states is a function of (C/ alpha ). Three upper limits for the number of bound states associated with the Yukawa potential are evaluated and compared. These three limits are those given by V. Bargmann, J. Schwinger, and Lieb. In addition, the Sobolev inequality states that whenever (C/ alpha ) less than 1. 65 no bound state occurs. This agrees to within a few percent of the numerical calculations of Bonch-Bruevich and Glasko. The V. Bargmann and Lieb limits and the Sobolev inequality are substantially easier to evaluate than the Schwinger limit.