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

TL;DR

This paper investigates the unique nonlinear supersymmetry in Poschl-Teller and Lame systems, revealing differences in their supercharges and uncovering how peculiar states encode key information about related quantum models.

Contribution

It clarifies the nature of peculiar states in Poschl-Teller systems using Lame equation, highlighting differences from Lame systems and their relation to free particles.

Findings

Supercharges in Poschl-Teller include nonphysical states.

Peculiar states encode information about hyperbolic, trigonometric, and free particle systems.

Differences in supersymmetry between Poschl-Teller and Lame systems are elucidated.

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.