International Journal of Theoretical Physics ( IF 1.4 ) Pub Date : 2021-03-24 , DOI: 10.1007/s10773-020-04667-y Fethi Bouzeffour , Wissem Jedidi
In this paper we first construct an analytic realization of the Cλ-extended oscillator algebra with the help of difference-differential operators. Secondly, we study families of d-orthogonal polynomials which are extensions of the Hermite and Laguerre polynomials. The underlying algebraic framework allowed us a systematic derivation of their main properties such as recurrence relations, difference-differential equations, lowering and rising operators and generating functions. Finally, we use these polynomials to construct a realization of the Cλ-extended oscillator by block matrices.
中文翻译:
Cλ-扩展的振荡器代数和d-正交多项式
在本文中,我们首先构建一个分析实现的Ç λ -Extended振荡器代数差微分算子的帮助。其次,我们研究d正交多项式的族,这是Hermite和Laguerre多项式的扩展。潜在的代数框架使我们能够系统地推导其主要性质,例如递归关系,差分-微分方程,运算符的下降和上升以及生成函数。最后,我们使用这些多项式来构造实现的Ç λ由块矩阵-Extended振荡器。