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Supersymmetric partners and confinement of a spiked inverted oscillator model

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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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Authors and Affiliations

  1. Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, USA

    Axel Schulze-Halberg

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  1. Axel Schulze-Halberg
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Correspondence to Axel Schulze-Halberg.

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Schulze-Halberg, A. Supersymmetric partners and confinement of a spiked inverted oscillator model. Eur. Phys. J. Plus 130, 228 (2015). https://doi.org/10.1140/epjp/i2015-15228-8

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  • DOI: https://doi.org/10.1140/epjp/i2015-15228-8

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