Developing Special Functions tools for contemporary problems in physics

为当代物理学问题开发特殊函数工具

• 批准号: RGPIN-2016-03728
• 负责人: Saad, Nasser
• 金额: $ 1.6万
• 依托单位: University of Prince Edward Island
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=633110
• 关键词: Developing; Special; Functions; tools; contemporary

`Special functions' are mathematical functions that arise from solving `special' problems in physics. It is known that many physical and real-world phenomena modeled using differential equations. Specifically, various quantum systems reduced to the analysis of second-order differential equations with polynomial coefficients. Until a few decades ago, the theory of special functions was considered exhausted with well-established results entirely available to physicists. Recently, however, new trends in physics emerged, for instance: Supersymmetry, Supergravity, Integrable systems, Quantum confined systems, Quantization techniques, Coherent states, and Factorization method (Darboux transformations, Bi-spectrality), that required innovative techniques to study them.

“特殊函数”是在解决物理学中的“特殊”问题时产生的数学函数。众所周知，许多物理和现实世界的现象都是用微分方程式建模的。具体地说，各种量子系统归结为分析具有多项式系数的二阶微分方程组。直到几十年前，特殊函数理论还被认为已经穷途末路，物理学家完全可以得到公认的结果。然而，最近物理学出现了新的趋势，例如：超对称性、超重力、可积系统、量子受限系统、量子化技术、相干态和因式分解方法(达布变换、双谱)，这些都需要创新的技术来研究它们。