Solution of Two-Body Bound State Problems with Confining Potentials

Abstract

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark $({\rm Y}(b\bar{b}),\psi (c\bar{c}))$, are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results.

Comments: 6 pages, 5 tables