Bound and scattering state solutions of a hyperbolic-type potential

A hyperbolic-type potential with a centrifugal term is solved approximately using the path integral approach. The radial Green's function is expressed in closed form, from which the energy spectrum and the suitably normalized wave functions of bound and scattering states are extracted for (1/2) - root(1/4) - (h(2)alpha(2)/2 mu D)l(l + 1) < sigma < (1/2) + root(1/4) - (h(2)alpha(2)/2 mu D)l(l + 1). Besides, the phase shift and the scattering function Sl for each angular momentum l are deduced. The particular cases corresponding to the s-waves (l = 0) and the barrier potential (sigma = 1) are also analyzed.