A new class of coherent states involving Fox-Wright functions and their generalization in the bicomplex framework

TL;DR

This paper introduces a new class of coherent states based on Fox Wright functions, extending them into the bicomplex framework and analyzing their properties for both discrete and continuous spectra.

Contribution

It develops Fox Wright coherent states with normalization functions, extends them to bicomplex arguments, and generalizes their properties within this new mathematical setting.

Findings

Coherent states satisfy continuity, normalizability, and resolution of unity.

Bicomplex Fox Wright functions enable the construction of states in the bicomplex setting.

Generalization of results to bicomplex framework broadens potential applications.

Abstract

In this work, an extensive class of coherent states is introduced by taking the Fox Wright function as the normalization function. It is demonstrated that these states satisfy the key requirements of continuity, normalizability and resolution of unity. Furthermore, coherent states associated with the continuous spectrum are obtained through a discrete to continuous limiting procedure. Moreover, FW generalized multi parameter nu function is introduced and shown to act as the normalization function for the Fox Wright coherent states in the continuous spectrum. Later the Fox Wright function with bicomplex arguments has been introduced and its existence has been investigated. Bicomplex Fox Wright coherent states are also developed for the discrete spectrum based on this new function and their properties are analyzed. Subsequently, the results regarding Fox Wright coherent states are generalized to the bicomplex setting. In addition, a bicomplex FW generalized multi-parameter nu function is defined to demonstrate that it provides the normalization for these states in the continuous spectrum.