Complementarity vs coordinate transformations: Mapping between pseudo-Hermiticity and weak pseudo-Hermiticity
Year: 2021
Type: article
Abstract: We investigate in this paper the concept of complementarity, introduced by Bagchi and Quesne [Phys. Lett. A 301, 173 (2002)], between pseudo-Hermiticity and weak pseudo-Hermiticity in a rigorous mathematical viewpoint of coordinate transformations when a system has a position-dependent mass. We first determine, under the modified-momentum, the generating functions identifying the complexified potentials V±(x) under both concepts of pseudo-Hermiticity η̃+ (respectively, weak pseudo-Hermiticity η̃−). We show that the concept of complementarity can be understood and interpreted as a coordinate transformation through their respective generating functions. As a consequence, a similarity transformation that implements coordinate transformations is obtained. We show that the similarity transformation is set up as a fundamental relationship connecting both η̃+ and η̃−. A special factorization η+=η−†η− is discussed in the constant mass case, and some Bäcklund transformations are derived.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0036401
Authors: Samira Saidani, Sid-Ahmed Yahiaoui
Institution: University of Blida
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3097201143