New generalized Hermite polynomials with three variables obtained via quantum optics method and their applications
Year: 2025
Type: article
Abstract: Special polynomials (e.g. Hermite polynomials) are very important for the development of physics and mathematics. As a further extension of ordinary Hermite polynomials, we introduce new generalized Hermite polynomials with three variables and find their generating functions using the operator ordering method in quantum optics. Also, some new operator identities and integral formulas are obtained. As applications, the normalization, Wigner functions and evolutions for certain quantum states are analytically presented. These analytical results can provide conveniences for numerically studying the properties and applications of such quantum states.
Source: Lithuanian Journal of Physics
Authors: An-peng Wang, Yi-xing Wang
Institutions: Shandong Huayu University of Technology, Linyi University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413129265