Eur. Phys. J. Plus (2021) 136: 668
https://doi.org/10.1140/epjp/s13360-021-01642-2

Regular Article

Dirac-like Hamiltonians associated to Schrödinger factorizations

¹ Department of Medical Services and Techniques, Ankara Medipol University, 06050, Ankara, Turkey
² Department of Physics, Faculty of Science, Ankara University, 06100, Ankara, Turkey
³ Departamento de Física Teórica, Atómica y Óptica, and IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain

^b sengul.kuru@science.ankara.edu.tr

Received: 10 April 2021
Accepted: 4 June 2021
Published online: 17 June 2021

Abstract

In this work, we have extended the factorization method of scalar shape-invariant Schrödinger Hamiltonians to a class of Dirac-like matrix Hamiltonians. The intertwining operators of the Schrödinger equations have been implemented in the Dirac-like shape invariant equations. We have considered also another kind of anti-intertwining operators changing the sign of energy. The Dirac-like Hamiltonians can be obtained from reduction of higher dimensional spin systems. Two examples have been worked out, one obtained from the sphere ${\mathcal{S}}^2$ and a second one, having a non-Hermitian character, from the hyperbolic space ${\mathcal{H}}^2$.