When did Modern Physics begin? In 1834 Hamilton could have derived the Schrödinger equation if he had any experimental evidence that particles were also waves. The word "eikonal" comes from an ancient Greek word that we know as "icon", which means "image". Hamilton was working on optics when made this approximation in an attempt to model the behavior of light as it passes through a medium in which the index of refraction varies smoothly. This is an alternate derivation of what physics majors know as the Ehrenfest theorem, restricted to one-dimension so that a very simple proof can be constructed.
