标题： 一种新的变形厄米多项式及其应用 显示英文标题

标题： A New Kind of Deformed Hermite Polynomials and Its Applications

摘要： 最近，在研究para玻色坐标表示时引入了一种新的变形微积分。基于这种变形微积分，本文提出Hermite多项式的一种新变形，并讨论了它的若干性质，如生成函数、正交归一性、微分和积分表示以及递推关系。作为其应用，我们计算了para玻色压缩数态的显式形式，导出了para玻色振幅平方压缩的一组特别简单的最小不确定性态子集，并讨论了它们的基本压缩行为。 显示英文摘要

摘要： 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.