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

摘要

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/dx Also, by changing the derivative d/dx by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator H-SIO = -1/2 d(2)/dx(2) - 1/2x(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.