Bridging supersymmetric quantum mechanics, Heun's equation and the asymptotic iteration method

连接超对称量子力学、Heun 方程和渐近迭代方法

• 批准号: 249507-2011
• 负责人: Saad, Nasser
• 金额: $ 1.67万
• 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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=570632
• 关键词: Bridging; supersymmetric; quantum; mechanics; Heun

The proposed research program aims to bridge three areas of mathematical physics: Supersymmetric quantum mechanics, Heun's differential equations, and the asymptotic iteration method. By bridging, I mean finding, establishing, and solidifying connections and links among these three disciplines. The importance of this research program comes from the applications of its findings in a number of different areas of mathematical physics. Indeed, the recent developments in nanotechnology have renewed interest in the modeling of spatially confined quantum systems under the influence of a wide variety of confining potentials. The findings of the present program are expected to contribute substantially in this direction. Further, the recent applications of Heun's different equations in general relativity, quantum-, plasma-, atomic-, molecular-, and nano-physics indicates the need for a fresh and comprehensive approach to the study of this class of equations. In order to achieve this bridging, the plan is to implement supersymmetric quantum mechanics techniques in the study of Heun's differential equations and to analyze their solutions further by using the asymptotic iteration method. The purpose is to span these three topics in as unified and concise way as possible in order to gain a better understanding of the theory of supersymmetric quantum mechanics.

拟议的研究计划旨在弥合数学物理的三个领域：超对称量子力学，Heun微分方程和渐近迭代方法。我所说的桥梁，是指在这三个学科之间找到、建立和巩固联系和纽带。 这项研究计划的重要性来自于它的发现在数学物理的许多不同领域的应用。事实上，纳米技术的最新发展重新引起了人们的兴趣， 在各种各样的限制势的影响下，空间限制量子系统的建模。预计本方案的研究结果将在这方面作出重大贡献。此外，最近Heun的不同方程在广义相对论，量子，等离子体，原子，分子和纳米物理学中的应用表明需要一种新的和全面的方法来研究这类方程。 为了实现这种桥接，计划是实施超对称量子力学技术 在Heun微分方程研究中的应用，并进一步用渐近迭代法分析其解。目的是尽可能统一和简明地跨越这三个主题，以便更好地理解超对称量子力学理论。