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Routledge eBooks

Teaching quantum physics to middle and high-school students using phasor wheels

R. K. Choudhary, D. G. Blair

Published Aug 13, 2021• 0 citations
Publisher

Abstract

This chapter introduces the powerful Feynman path integral approach to quantum mechanics. It is intended for readers who are interested in a non-mathematical approach to quantum physics at the middle and high-school level. Einstein's discovery of light quanta played a major role in the birth of quantum mechanics. Einstein made the bold prediction that light comes as a stream of particles called “light quanta”. Photons, like bullets, carry momentum that applies forces to mechanical objects. The method of phasors that, the authors applied to radio waves works equally for visible photons and even for particles such as electrons and molecules. Feynman's method of all possible paths assumes a large number of possible paths. Single-photon counting experiments and laser technology allow the reader to see deeply into the quantum world. The videos of single-particle interference consolidate the idea of photons and their intrinsic randomness.

DOI
10.4324/9781003161721-20

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This chapter introduces the powerful Feynman path integral approach to quantum mechanics. It is intended for readers who are interested in a non-mathematical approach to quantum physics at the middle and high-school level. Einstein's discovery of light quanta played a major role in the birth of quantum mechanics. Einstein made the bold prediction that light comes as a stream of particles called “light quanta”. Photons, like bullets, carry momentum that applies forces to mechanical objects. The method of phasors that, the authors applied to radio waves works equally for visible photons and even for particles such as electrons and molecules. Feynman's method of all possible paths assumes a large number of possible paths. Single-photon counting experiments and laser technology allow the reader to see deeply into the quantum world. The videos of single-particle interference consolidate the idea of photons and their intrinsic randomness.
Abstract Quantum electrodynamics was described by Feynman as the ‘jewel of physics’ [1985 QED: The Strange Theory of Light and Matter (Alix G. Mautner Memorial Lectures) (Princeton, NJ: Princeton University Press)] because of its ability to precisely describe the interaction of light and matter. It embodies the key concepts of quantum physics and yet also describes classical optics. It is normally considered to be too advanced for use in schools. Here we show that through the use of novel learning tools called phasor wheels , it is possible to make quantum electrodynamics accessible to students from middle school and higher. Our graphical approach is based on the summation of all possible paths (formally known as Feynman path integrals). It uses graphical vector addition, and gives students a deep understanding of vectors. It offers insights into the quantum world in which observations represent quantum probability density, while correctly describing the laws of classical optics. The phasor wheel is a tactile tool that allows students to compute the probability of photons arriving at a point in space and to explore phenomena such as matter–wave interference, diffraction, and reflection without any distinction between quantum or classical. To make it accessible, we combine the phasor tool with real-life analogies, and videos of single quanta interference. Needing only elementary mathematics, the approach is suitable for middle/upper secondary schools as well early undergraduate students.
This chapter traces the sequence of discoveries which convinced physicists of the need to replace classical theories of light and matter. It is intended for readers who wish to learn how Einsteinian physics emerged through a sequence of discoveries that led the reader to the frontiers of current knowledge. The highlights the enormous struggle from which the revolutionary new understanding of the universe called Einsteinian physics emerged. Traditionally, quantum physics and general relativity have stood apart, separated by a fundamental mismatch between their language, their mathematics, and their structure. Einstein's conclusion made the conundrum of quantum physics quite clear. Photons behaved like particles with discrete energy. To provide some sense of a mechanism for understanding quantum behavior, Schrodinger and Bohr developed the Copenhagen interpretation of quantum physics. From a few small clues, Einstein and others realized that sound, heat, and light come in energy packets called phonons and photons.
We outline an introduction to quantum mechanics based on the sum-over-paths method originated by Richard P. Feynman. Students use software with a graphics interface to model sums associated with multiple paths for photons and electrons, leading to the concepts of electron wavefunction, the propagator, bound states, and stationary states. Material in the first portion of this outline has been tried with an audience of high-school science teachers. These students were enthusiastic about the treatment, and we feel that it has promise for the education of physicists and other scientists, as well as for distribution to a wider audience. © 1998 American Institute of Physics.
This introductory text emphasizes Feynman's development of path integrals and its application to wave theory for particles. Suitable for undergraduate and graduate students of physics, the well-written, clear, and rigorous text was written by two of the nation's leading authorities on quantum physics. A solid foundation in quantum mechanics and atomic physics is assumed. Early chapters provide background in the mathematical treatment and particular properties of ordinary wave motion that also apply to particle motion. The close relation of quantum theory to physical optics is stressed. Subsequent sections emphasize the physical consequences of a wave theory of material properties, and they offer extensive applications in atomic physics, nuclear physics, solid state physics, and diatomic molecules. Four helpful Appendixes supplement the text.
We formulate a didactic proposal for introducing some fundamental concepts of quantum physics to advanced high school students, and to their teachers. The inspiration comes from some of the fundamental papers about the subject by Albert Einstein, in which many of these concepts, for example light quanta, wave-particle duality, and probability, were introduced for the first time, in a characteristically illuminating way. The proposal can be supplemented by a discussion of elementary tools of statistical physics, which are needed at some point. Preliminary results, both with students and teachers, are very promising.