Collected papers on Wave Mechanics

Before we go on to consider the problem of proper values for further special systems, let us throw more light on the general correspondence which exists between the Hamiltonian-Jacobi differential equation of a mechanical problem and the “allied” wave equation … The inner connection between Hamilton’s theory and the process of wave propagation is anything but a new idea. It was not only well known to Hamilton, but it also served him as the starting-point for his theory of mechanics, which grew out of his Optics of nonhomogeneous Media. Hamilton’s variational principle can be shown to correspond to Fermat’s Principle for this wave propagation. Unfortunately this powerful and momentous conception of Hamilton is deprived, in most modern reproductions, of its beautiful raiment as a superfluous accessory, in favor of a more colorless representation of the analytical correspondence. (p. 13)

Today, there are not a few physicists who … regard the task of physical theory as being merely a mathematical description (as economical as possible) of the empirical connections between observable quantities … without the intervention of unobservable elements. (Schrodinger, 1928, p. 58)