Abstract
We apply the formalism of supersymmetric quantum mechanics (SUSY) to an inverted oscillator system that has a singularity at the origin. SUSY partners of this spiked inverted oscillator model are constructed for both an unconfined and a confined scenario. We establish conditions for generating regular potentials, associated with bounded solutions. In the confined case, discrete spectral values of the spiked inverted oscillator model are computed, as well as for its standard counterpart that does not feature a singularity.
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