Common Pedagogical Issues with De Broglie Waves: Moving Double Slits, Composite Mass, and Clock Synchronization

Abstract

This paper addresses gaps identified in pedagogical studies of how misunderstanding of De Broglie waves affects later coursework and presents a heuristic for understanding the De Broglie frequency of composite. De Broglie’s little known derivation is reviewed with a new illustration based on his description. Simple techniques for reference frame independent analysis of a moving double slit electron interference experiment are not previously found in any literature and cement the concepts. Points of similarity and difference between De Broglie and Schrödinger waves are explained. The necessity of momentum, energy, and wavelength changes in the electrons in order for them to be vertically displaced in their own reference frame is shown to be required to make the double slit analysis work. A relativistic kinematic analysis of De Broglie frequency is provided showing how the higher De Broglie frequency of moving particles is consistent with Special Relativity and time dilation and that it demonstrates a natural system which obeys Einstein’s clock synchronization convention of simultaneity and no other. Students will be better prepared to identify practical approaches to solving problems and to think about fundamental questions.