Abstract

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Symmetry: Culture and Science
Volume 35, Number 3, pages 303-306 (2024)
https://doi.org/10.26830/symmetry_2024_3_303

HIGH-ORDER SUPERSYMMETRIC QUANTUM MECHANICS

Yajaira Concha-Sánchez^1*, Juan D. García-Muñoz², Alfredo Raya³

¹ Facultad de Ingeniería Civil, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C, Ciudad Universitaria, Francisco J. Mújica S/N. Col. Felícitas del Río, 58030, Morelia, Michoacán, Mexico
Email: yajaira.concha@umich.mx
ORCID: 0000-0001-8904-527X

² Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, Francisco J. Mújica S/N. Col. Felícitas del Río, 58040, Morelia, Michoacán, Mexico.
Email: juan.domingo.garcia@umich.mx
ORCID: 0000-0002-6906-1640

³ Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, Francisco J. Mújica S/N. Col. Felícitas del Río, 58040, Morelia, Michoacán, Mexico.
Email: alfredo.raya@umich.mx
ORCID: 0000-0002-5394-8634

^* corresponding author

Abstract: 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 . 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 (García-Muñoz, Raya and Concha-Sánchez, 2023).

Keywords: Riemann Zeta function, supersymmetric quantum mechanics, confluent algorithm

References:
Concha-Sánchez, Y., Díaz-Bautista, E. and Raya, A. (2022) Ritus functions for Graphene-like systems with magnetic fields generated by first-order intertwining operators. Physica Scripta, 97, 095203. https://doi.org/10.1088/1402-4896/ac8582

Das, A. and Kalauni P. (2019) Supersymmetry and the Riemann zeros on the critical line. Physics Letters B, 721, 265-269. https://doi.org/10.1016/j.physletb.2019.02.040

Fernandez, D. J. C., and Fernandez-Garcia, N. (2005) Higher order supersymmetric quantum mechanics. AIP Conference Proceeding p 744. https://doi.org/10.1063/1.1853203

García-Muñoz, J. D., Raya, A. and Concha-Sánchez, Y. (2023) High-order SUSY-QM, the quantum XP model zeroes of the Riemann Zeta function. Physica Scripta, 98, 125203. https://doi.org/10.1088/1402-4896/ad05ac