Discovering by analogy: the case of Schrödinger's equation

Abstract

Schrödinger's equation is derived by using Hamilton's mathematically unified treatment of geometrical optics and analytical mechanics. This is done by a didactically appropriate reconstruction of Schrödinger's approach, in which the formal similarity of the two theories is considered in the strict sense of the proportionality of the corresponding quantities in the two theories. This is taken as an example emphasizing the crucial role analogy arguments can play in the formulation of new physical ideas or theories and illustrating the role the knowledge of the historical development of a subject can play in its presentation.