A New Kind of Deformed Hermite Polynomials and Its Applications

TL;DR

This paper introduces a new deformation of Hermite polynomials based on deformed calculus, explores their properties, and applies them to analyze parabose squeezed states and their squeezing behaviors.

Contribution

It proposes a novel deformation of Hermite polynomials and applies this to quantum parabosonic systems, providing new tools for analyzing squeezed states.

Findings

Derived explicit forms of parabose squeezed number states

Identified a simple subset of minimum uncertainty states

Discussed squeezing behaviors of these states

Abstract

A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating function, orthonormality, differential and integral representaions, and recursion relations are also discussed in this paper. As its applications, we calculate explicit forms of parabose squeezed number states, derive a particularly simple subset of minimum uncertainty states for parabose amplitude-squared squeezing, and discuss their basic squeezing behaviours.