Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics

Abstract

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.

82 pages, fully revised, several references added

References in corpus (5)

• Light-Front Holographic QCD and Emerging Confinement
• New knotted solutions of Maxwell's equations
• Conformal theories including conformal gravity as gauge theories on the hypercone
• Black magic session of concordance: Regge mass spectrum from Casson's invariant
• Probabilistic vs optical interpretation of quantum mechanics

Cited by in corpus (4)

• Intermediate-range Casimir-Polder interaction probed by high-order slow atom diffraction
• Deterministic actions on stochastic ensembles of particles can replicate wavelike behaviour of quantum mechanics: does it matter?
• How the Modified Bertrand Theorem Explains Regularities and Anomalies of the Periodic Table of Elements
• Searching for high temperature superconductivity: From Mendeleev to Seiberg-Witten via Madelung and beyond