Two-step Shape Invariance in the Framework of N-fold Supersymmetry
arXiv:1203.4012 · doi:10.1140/epjp/i2015-15025-5
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.
31 pages, no figures
References in corpus (8)
- N-fold Supersymmetry in Quantum Systems with Position-dependent Mass
- Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics
- Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
- Fractional supersymmetry and hierarchy of shape invariant potentials
- Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry
- N-fold Supersymmetry in Quantum Mechanical Matrix Models
- N-fold Supersymmetric Quantum Mechanics with Reflections
- Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry II. The N=3 Case