Peculiarities of the hidden nonlinear supersymmetry of Poschl-Teller system in the light of Lame equation

Abstract

A hidden nonlinear bosonized supersymmetry was revealed recently in Poschl-Teller and finite-gap Lame 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 Poschl-Teller system, unlike the case of Lame equation, includes nonphysical states. By means of Lame equation, we clarify the nature of these peculiar states, and show that they encode essential information not only on the original hyperbolic Poschl-Teller system, but also on its singular hyperbolic and trigonometric modifications, and reflect the intimate relation of the model to a free particle system.

10 pages, typos corrected; to appear in J. Phys. A

References in corpus (3)

• Hidden supersymmetry in quantum bosonic systems
• Hidden nonlinear supersymmetry of finite-gap Lame equation
• A new effective mass Hamiltonian and associated Lame equation: bound states

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• Spectral singularities in PT-symmetric periodic finite-gap systems
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Conformal bridge transformation and PT symmetry
• Coupled system of Dirac fermions with different Fermi velocities via composites of SUSY operators