Deformed Boson Algebras and $\mathcal{W}_{\alpha,\beta,\nu}$-Coherent States: A New Quantum Framework

TL;DR

This paper introduces a new class of coherent states based on a deformed boson algebra involving advanced special functions, analyzing their mathematical properties and potential applications in quantum physics.

Contribution

It develops a novel framework for coherent states using a generalized algebra with special functions, expanding the theoretical landscape of quantum state construction.

Findings

States exhibit continuity and completeness properties.

Resolution of the Stieltjes moment problem achieved.

Potential applications in quantum optics and fractional quantum mechanics.

Abstract

We introduce a novel class of coherent states, termed $\mathcal{W}^{(\bar{\alpha},\bar{\nu})}(z)$-coherent states, constructed using a deformed boson algebra based on the generalized factorial $[n]_{\alpha,\beta,\nu}!$. This algebra extends conventional factorials, incorporating advanced special functions such as the Mittag-Leffler and Wright functions, enabling the exploration of a broader class of quantum states. The mathematical properties of these states, including their continuity, completeness, and quantum fluctuations, are analyzed. A key aspect of this work is the resolution of the Stieltjes moment problem associated with these states, achieved through the inverse Mellin transformation method. The framework provides insights into the interplay between classical and quantum regimes, with potential applications in quantum optics and fractional quantum mechanics. By extending the theoretical landscape of coherent states, this study opens avenues for further exploration in mathematical physics and quantum technologies.