Energy Eigenvalues for the Coulomb Potential with Cut-Off. Part I.

In this paper, the Schr\"odinger equation is solved analytically for the Coulomb potential with horizontal cut-off. For this purpose, a detailed mathematical study of the confluent hypergeometric functions is carried out and their similarity to Bessel and Neumann functions is put on a quantitative basis. The resulting formulas for the energy levels are valid for all cases except when the energy is lying very little above the cut-off.