Meixner random variables and their quantum operators

TL;DR

This paper explores the quantum operator representations of Meixner random variables, providing a new characterization through their position-momentum decomposition involving translation operators.

Contribution

It introduces a novel quantum operator framework for Meixner random variables using position-momentum decomposition and translation operators.

Findings

New quantum operator representation of Meixner variables

Characterization of these variables via position-momentum decomposition

Use of translation operators in the new framework

Abstract

We find the position-momentum decomposition of the quantum operators of the classic Meixner random variables. The position-momentum decomposition involves translation operators, which are used to give a new characterization of the Meixner random variables.