Abstract

A hidden nonlinear bosonized supersymmetry was revealed recently in the Pöschl-Teller and finite-gap Lamé systems. In spite of the intimate relationship between the two quantum models, the hidden supersymmetry in them displays essential differences. In particular, the kernel of the supercharges of the Pöschl-Teller system, unlike the case of the Lamé equation, includes nonphysical states. By means of the Lamé equation, we clarify the nature of these peculiar states, and show that they encode essential information not only on the original hyperbolic Pöschl-Teller system, but also on its singular hyperbolic and trigonometric modifications, and reflect the intimate relation of the model to a free-particle system. © 2007 IOP Publishing Ltd.