A Note on the Wave Mechanics of Matter

P. J. Daniell

Donald C. Chang

Paul A. Hanle

Unpublished letters of late 1925 between Einstein and Schrödinger and the doctoral thesis of de Broglie reveal sources of Schrödinger’s inspiration to invent wave mechanics. Schrödinger saw a congenial similarity of de Broglie’s work on the stability of the atom with his own earlier speculation in relativity, which he noted to Einstein. But the last chapter of de Broglie’s thesis, on quantum statistics of gases, which is unfamiliar to many modern readers, provided Schrödinger with the method of treatment of a gas of material particles considered as a system of modes of vibration, of ’’matter waves.’’ This method especially, and other successes of de Broglie’s ’’ingenious thesis,’’ convinced Schrödinger to take seriously the first part, on the conditions of stability of the atom in a wave picture. Thus he sought and found an equation to describe the states of the electron from the matter-wave viewpoint.

Roshan Raj

A derivation of the Klein-Gordon wave equation without substituting the corresponding quantum mechanical energy and momentum operators in Einstein's relativistic energy-momentum relationship is presented. An additional discussion is made to motivate readers to understand the distinction between the quantum wave equation and the governing law in the context of quantum mechanical formalisms. A resemblance of mathematical structure between the Maxwell wave equation and the deduced Klein-Gordan equation is shown. It is also noted that the wave velocity of the matter wave becomes equal to photon velocity for massless cases. This can be useful to explain why light equally shows matter and particle behaviour.

Louis de Broglie