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.
Highlights
At some point the undergraduate physics student and many engineering or chemistry students as well will take a one semester course in quantum mechanics (QM)
Many bring incorrect ideas from misunderstanding optics to bear on electrons, such as thinking photons “bend at the slit edges” in diffraction, and compound their misunderstanding by “failure to recognize the De Broglie wave is not an inherent property of an electron but varies with momentum,” thinking that “diffraction and interference are independent of velocity,” and believing that “equations that apply to the wavelength of light apply to De Broglie wavelength” [1]
In the whirlwind of new information and possibly persistent misconceptions from prior courses, students may not even verbalize the puzzle and if they do, instructors may find themselves surprised and unsure how to answer. In this way a vague sense of mystery is unnecessarily passed to the generation, and occasionally discussions about how to apply the Lorentz transform to a De Broglie wavelength crop up on physics discussion forums [5]. Such discussions never mention that De Broglie derived the wavelength as an artifact of the Lorentz transformation of a wave of simultaneity, resulting in the desynchronization of clocks seen by relatively moving observers, because this historical derivation is not one of the minimal sets captured by and repeated in QM textbooks, most of which seem to follow very similar outlines
Summary
At some point the undergraduate physics student and many engineering or chemistry students as well will take a one semester course in quantum mechanics (QM). In the whirlwind of new information and possibly persistent misconceptions from prior courses, students may not even verbalize the puzzle and if they do, instructors may find themselves surprised and unsure how to answer In this way a vague sense of mystery is unnecessarily passed to the generation, and occasionally discussions about how to apply the Lorentz transform to a De Broglie wavelength crop up on physics discussion forums [5]. Such discussions never mention that De Broglie derived the wavelength as an artifact of the Lorentz transformation of a wave of simultaneity, resulting in the desynchronization of clocks seen by relatively moving observers, because this historical derivation is not one of the minimal sets captured by and repeated in QM textbooks, most of which seem to follow very similar outlines. The limited theoretical work on this is analyzed and a simple heuristic developed which provides a satisfactory answer to first order
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
