NonHermitian inverted Harmonic OscillatorType Hamiltonians Generated from Supersymmetry with Reflections
Abstract
By modifying and generalizing known supersymmetric models we are able to find four different sets of onedimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to nonHermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for nonHermitian 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 annihilationtype 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 twobody Calogerotype model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given.
 Publication:

arXiv eprints
 Pub Date:
 July 2017
 arXiv:
 arXiv:1707.09082
 Bibcode:
 2017arXiv170709082M
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 Mod. Phys. Lett. A, 34 (2019) 1950028