The author argues that, for consistency, the de Broglie wavelength of a moving material particle should take account of the medium in which the particle is moving. Louis de Broglie posited that a moving material particle should be considered in the same way as a photon. Now, the wavelength of a photon is related to the medium in which it propagates and it seems only logical that, for a moving material particle the nature of the medium should be captured by the inclusion of something which characterizes that medium. It is shown that this 'something' is the index of refraction.
The de Broglie wavelength is then shown to be given by: l = h/p.r , where h is Planck's constant, p, the momentum of the particle and r, the index of refraction. Further, it is demonstrated that the inclusion of the index of refraction in the de Broglie wavelength alters Heisenberg's position/momentum relationship (but not the energy/time relationship), and, in addition, modifies the Schrödinger equations. All of these return to their commonly recognized forms when the index of refraction is set equal to its vacuum value.
Table of Contents
- Abstract
- Introduction
- Analysis - de Broglie
- The Fidler diagram
- Analysis-Heisenberg
- Discussion
- References
Objectives and Key Themes
The primary goal of this work is to demonstrate that the expression for the de Broglie wavelength of a moving material particle should incorporate the index of refraction of the medium it traverses, for consistency with the wave-particle duality concept.
- Revisiting the de Broglie hypothesis in light of medium properties.
- Modifying the de Broglie wavelength expression to include the refractive index.
- Analyzing the implications of this modification on Heisenberg's uncertainty principle.
- Examining the impact on Schrodinger's wave equations.
- Exploring the relationship between wave properties, medium characteristics, and the concept of wave-particle duality.
Chapter Summaries
- Introduction: This chapter provides a general overview of the de Broglie hypothesis and its experimental verification. It introduces the concept of wave-particle duality and lays the groundwork for the argument that the de Broglie wavelength should account for the medium's refractive index.
- Analysis - de Broglie: This chapter defines fundamental concepts of mechanics in Planck units and utilizes them to derive an expression for the de Broglie wavelength that incorporates the refractive index.
- The Fidler diagram: This chapter introduces the Fidler diagram, a tool developed for analyzing the behavior of photons in different media. It highlights the importance of the radiation Strouhal number and its relationship to the refractive index.
Keywords
Key concepts discussed in this work include the de Broglie hypothesis, wave-particle duality, refractive index, Heisenberg's uncertainty principle, Schrodinger's wave equation, Planck units, Fidler diagram, and radiation Strouhal number.
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- William Fidler (Autor), 2020, Werner Heisenberg, Louis de Broglie and Erwin Schrödinger revisited, Múnich, GRIN Verlag, https://www.grin.com/document/915006
