We analyze the one dimensional scattering produced by all variations of the Pöschl–Teller potential, i.e., potential well, low and high barriers. The transmission coefficients of Pöschl–Teller well and low barrier potentials have an infinite number of simple poles corresponding to bound and antibound states. However, the Pöschl–Teller high barrier potential shows an infinite number of resonance poles. We have constructed ladder operators connecting wave functions for bound and antibound states as well as for resonance states. Finally, using wave functions of these states, we provide some examples of supersymmetric partners of the Pöschl–Teller Hamiltonian.
