  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 Schr\"odinger 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.
