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Huygens triviality-a concept invented by Jacques Hadamard-describes anequivalence class connecting those 2nd order partial differential equationswhich are transformable into the wave equation. In this work it isdemonstrated, that the Schr\"odinger equation with the time-independentHamiltonian belongs to such an equivalence class. The wave equation is theequation for which Huygens' principle (HP) holds. The HP was a subject ofconfusion in both physics and mathematics literature for a long time. Notsurprisingly, the role of this principle was obscured from the beginnings ofquantum mechanics causing some theoretical and experimental misunderstandings.The purpose of this work is to bring the full clarity into this topic. By doingso, we obtained a large amount of new results related to uses of Lie spheregeometry, of twistors, of Dupin cyclides, of null electromagnetic fields, ofAdS-CFT correspondence, of Penrose limits, of geometric algebra, etc. inphysical problems ranging from the atomic to high energy physics and cosmology.

Huygens triviality of the time-independent Schr\"odinger equation. Applications to atomic and high energy physics