Abstract
A derivation of the S-matrix for the Pöschl-Teller and related potentials is done by group-theoretical methods using the group SU(1,1), the dynamical symmetry for these systems. Light is shed on the representation of SU(1,1) which must be used to this end, and the nature of bound (and anti-bound or virtual) states viewed as poles of the S-matrix in the complex plane.
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