Applications of Generalized Coherent States

A. M. Perelomov

A. M. Perelomov

Muhammad Arif Sadiq

John R. Klauder

The area of applicability of coherent states is generally quantum theory, while that of wavelets is generally signal analysis. Nevertheless, separated from their respective applications, coherent states and (continuous) wavelets have a great deal in common. To illustrate this connection we shall outline three general types of coherent states and a few of their applications. We address our presentation to interested wavelet practitioners.

Dušan Popov

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.

A. D. Jannussis, G. Karayannis, Παναγιώτης Παναγόπουλος +1 more