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arXiv · 1203.4012

Two-step Shape Invariance in the Framework of N-fold Supersymmetry

Barnana Roy·Toshiaki Tanaka
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Abstract

We extensively investigate two-step shape invariance in the framework of N-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.

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BibTeXRIS

Barnana Roy, Toshiaki Tanaka. 2012-03-19. Two-step Shape Invariance in the Framework of N-fold Supersymmetry. https://doi.org/10.1140/epjp/i2015-15025-5

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