Eur. Phys. J. Plus (2015) 130: 25
https://doi.org/10.1140/epjp/i2015-15025-5

Regular Article

Two-step shape invariance in the framework of -fold supersymmetry

¹ Physics and Applied Mathematics Unit, Indian Statistical Institute, 700108, Kalkata, India
² Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, 305-0801, Ibaraki, Japan

^* e-mail: barnana@isical.ac.in

Received: 1 August 2014
Accepted: 10 December 2014
Published online: 10 February 2015

Abstract

We extensively investigate two-step shape invariance in the framework of -fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has second-order parasupersymmetry as well. Employing the general form of type A 2-fold supersymmetry, we systematically construct two-step shape-invariant potentials. In addition to the well-known ordinary shape-invariant potentials, we obtain several new and novel two-step shape-invariant ones which are not ordinary shape invariant. Furthermore, some of the latter potentials are conditionally two-step shape invariant and thus are conditionally solvable.