### Abstract

We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V± (z)=-U(z) 2 ±z(ddz)U(z) where U(z) k>0 k zk. In particular, we consider the cases generated by U(z)=z and z(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.

Original language | English (US) |
---|---|

Article number | 092108 |

Journal | Journal of Mathematical Physics |

Volume | 48 |

Issue number | 9 |

DOIs | |

State | Published - Oct 8 2007 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'Supersymmetric biorthogonal quantum systems'. Together they form a unique fingerprint.

## Cite this

Curtright, T., Mezincescu, L., & Schuster, D. (2007). Supersymmetric biorthogonal quantum systems.

*Journal of Mathematical Physics*,*48*(9), [092108]. https://doi.org/10.1063/1.2191367