Peculiarities of the hidden nonlinear supersymmetry of the Pöschl Teller system in the light of the Lamé equation
Abstract
A hidden nonlinear bosonized supersymmetry was revealed recently in the PöschlTeller and finitegap 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 PöschlTeller 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 PöschlTeller system, but also on its singular hyperbolic and trigonometric modifications, and reflect the intimate relation of the model to a freeparticle system.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2007
 DOI:
 10.1088/17518113/40/48/007
 arXiv:
 arXiv:0706.1114
 Bibcode:
 2007JPhA...4014403C
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Quantum Physics
 EPrint:
 10 pages, typos corrected