1. Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections.
- Author
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Mota, R. D., Ojeda-Guillén, D., Salazar-Ramírez, M., and Granados, V. D.
- Subjects
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HARMONIC oscillators , *SUPERSYMMETRY , *QUANTUM mechanics , *PARAMETER estimation , *MATHEMATICAL models - Abstract
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 d d x . Also, by changing the derivative d d x by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator H SIO = − 1 2 d 2 d x 2 − 1 2 x 2 , 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. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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