2024/04/19 by Popov, Dušan
#33C90 Applications of hypergeometric functions #81Qxx General mathematical topics and methods in quantum theory #81R30 Coherent states #FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2404.13119
In this paper we examine one of the multiple applications of the theta operator xd/dx in quantum mechanics, namely, in the formalism of generalized hypergeometric coherent states (GHG CSs). These states are the most general coherent states, in the sense that from them, through particularization, all coherent states with physical meaning can be obtained. A series of new results were obtained and some already known ones were found / confirmed (the integral representations, as well as the Laplace transform of hypergeometric functions). To support the theoretical considerations presented above, we examined, as example, the quantum systems with a linear energy spectrum. The results obtained in this paper contribute to widening the area of applicability of the theta operator.