HIGH-ORDER SUPERSYMMETRIC QUANTUM MECHANICS

In Quantum Mechanics, there exists the so-called supersymmetric algebra. In this work, we construct quantum mechanical Hamiltonians whose spectra are related to the Riemann Zeta function zeta(s). Such Hamiltonians are generated with first- and second- order confluent algorithms of supersymmetric quantum mechanics (SUSY-QM) departing from the Das and Kalauni (DK) model (Das and Kalauni, 2019), as a seed solution for our algorithms. We further find that unlike the DK case, where the SUSY-QM partner potentials correspond to free particles, our partner potentials belong to the family of inverse squared distance potentials with complex coupling (Garcia-Munoz, Raya and Concha-S & aacute;nchez, 2023).