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: This email address is being protected from spambots. You need JavaScript enabled to view it.
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.
Present address: Department of Physics, Faculty of Science, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, 112-8610, Tokyo, Japan
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2015
