与时间无关的薛定谔方程的惠更斯平凡性。原子物理和高能物理的应用
Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics
摘要：
Huygens平凡性是由Jacques Hadamard提出的一个概念，它描述了一个等价类，连接了可变换为波动方程的二阶偏微分方程。本文证明了哈密顿量与时间无关的薛定谔方程属于这样一个等价类。波动方程是惠更斯原理（HP）成立的方程。惠普是一个主题的混乱，在物理和数学文学很长一段时间。毫不奇怪，这个原理的作用从量子力学开始就被掩盖了，造成了一些理论和实验上的误解。这项工作的目的是使这一主题完全清晰。通过这样做，我们获得了大量的新结果，涉及到李球几何，扭曲，Dupin cylides，零电磁场，AdS-CFT对应，Penrose极限，几何代数等的应用，从原子到高能物理和宇宙学的物理问题。
英文摘要：
Huygens triviality-a concept invented by Jacques Hadamard-describes an equivalence class connecting those 2nd order partial differential equations which are transformable into the wave equation. In this work it is demonstrated, that the Schrödinger equation with the time-independent Hamiltonian belongs to such an equivalence class. The wave equation is the equation for which Huygens' principle (HP) holds. The HP was a subject of confusion in both physics and mathematics literature for a long time. Not surprisingly, the role of this principle was obscured from the beginnings of quantum mechanics causing some theoretical and experimental misunderstandings. The purpose of this work is to bring the full clarity into this topic. By doing so, we obtained a large amount of new results related to uses of Lie sphere geometry, of twistors, of Dupin cyclides, of null electromagnetic fields, of AdS-CFT correspondence, of Penrose limits, of geometric algebra, etc. in physical problems ranging from the atomic to high energy physics and cosmology.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
