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arXiv · 1707.09082

Non-Hermitian inverted Harmonic Oscillator-Type Hamiltonians Generated from Supersymmetry with Reflections

R. D. Mota·D. Ojeda-Guillén·M. Salazar-Ramírez·V. D. Granados
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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 $\frac{d}{dx}$. Also, by changing the derivative $\frac{d}{dx}$ by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted Harmonic oscillator $H_{SIO}=-\frac{1}{2}\frac{d^2}{dx^2}-\frac{1}{2}x^2$, 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.

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R. D. Mota, D. Ojeda-Guillén, M. Salazar-Ramírez, V. D. Granados. 2017-07-28. Non-Hermitian inverted Harmonic Oscillator-Type Hamiltonians Generated from Supersymmetry with Reflections. https://doi.org/10.1142/s0217732319500287

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