• DOI:10.1142/S0217732319500287
• Corpus ID: 119636939

Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections

@article{Mota2017NonHermitianIH,
  title={Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections},
  author={R. D. Mota and D. Ojeda-Guill'en and M. Salazar-Ram'irez and V{\'i}ctor David Granados},
  journal={Modern Physics Letters A},
  year={2017}
}

• R. D. Mota, D. Ojeda-Guill'en, +1 author V. Granados
• Published 28 July 2017
• Physics
• Modern Physics Letters A

By modifying and generalizing known supersymmetric models, we are able to find four different sets of one-dimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to non-Hermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for non-Hermitian supercharges with the Dunkl derivative instead of [Formula: see text]. Also, by changing the derivative [Formula: see text] by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator [Formula: see text], we generate the third set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a parameter of the supersymmetric two-body Calogero-type model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given.