Eur. Phys. J. Plus (2015) 130: 228
https://doi.org/10.1140/epjp/i2015-15228-8

Regular Article

Supersymmetric partners and confinement of a spiked inverted oscillator model

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

^* e-mail: axgeschu@iun.edu

Received: 4 September 2015
Accepted: 6 October 2015
Published online: 17 November 2015

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.