### Abstract

Scattering on the -symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex x plane from below. This trajectory reflects symmetry, sets the appropriate boundary conditions for bound states and also allows the restoration of the correct sign of the energy eigenvalues. Scattering states are composed from the two linearly independent solutions valid for non-integer values of the 2L parameter, which would correspond to the angular momentum in the usual Hermitian setting. The transmission and reflection coefficients are written in a closed analytic form, and it is shown that, similar to other -symmetric scattering systems, the latter exhibit the handedness effect. Bound-state energies are recovered from the poles of the transmission coefficients.

Original language | English |
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Article number | 295201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 29 |

DOIs | |

Publication status | Published - Jan 1 2009 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(29), [295201]. https://doi.org/10.1088/1751-8113/42/29/295201