Title: Analytical solutions for the radial Scarf II potential,
Abstract: The real Scarf II potential is discussed as a radial problem. This potential
has been studied extensively as a one-dimensional problem, and now these
results are used to construct its bound and resonance solutions for $l=0$ by
setting the origin at some arbitrary value of the coordinate. The solutions
with appropriate boundary conditions are composed as the linear combination of
the two independent solutions of the Schrödinger equation. The asymptotic
expression of these solutions is used to construct the $S_0(k)$ s-wave
$S$-matrix, the poles of which supply the $k$ values corresponding to the
bound, resonance and anti-bound solutions. The location of the discrete energy
eigenvalues is analyzed, and the relation of the solutions of the radial and
one-dimensional Scarf II potentials is discussed. It is shown that the
generalized Woods--Saxon potential can be generated from the Rosen--Morse II
potential in the same way as the radial Scarf II potential is obtained from its
one-dimensional correspondent. Based on this analogy, possible applications are
also pointed out.