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Electronic Conference on Universe (ECU)

A Proposal for Introducing Quantum Physics in the Footsteps of Einstein

Marco Di Mauro, Salvatore Esposito, Adele Naddeo

Published Feb 22, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.3390/ecu2021-09320

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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.
Teaching and learning QM at high school as well as the undergraduate level is a highly non-trivial task. Indeed, major changes are required in understanding the new physical reality, and students have to deal with counterintuitive concepts such as uncertainty and entanglement as well as advanced mathematical tools. In order to overcome these critical issues, a simple approach is presented here, which is based solely on two-vector and 2 × 2 matrix algebra. Furthermore, it could also enable educational institutions to fill the gap between high school curricula and the current scientific and technological advances in physics by allowing students to gain some insight into topics such as qubits and quantum computers. The inspiration behind our proposal as well as its firm theoretical foundation are based on the famous Umdeutung (reinterpretation) paper by W. Heisenberg, which introduces QM in matrix form.
Abstract This book provides the reader with a contemporary and comprehensive introduction to Quantum Mechanics. It is suitable for beginners as well as for more advanced university students. Quantum mechanics is presented in a pedagogical fashion, with a clear logical organization. The various concepts and methods are introduced first in elementary terms, and later developed into more precise formulations. Systematic studies of approximation methods and the discussion of a wide class of physical applications follow. Part I of the book, together with the opening sections of Part II, provide adequate material for an introductory course of one semester at most universities. The rest of the book might be used in an advanced course on Quantum Mechanics. The basic material is fairly standard, even though some discussions such as those on general systems with time-dependent Hamiltonians, on metastable systems, as well as the discussions in some of the Complement sections, may not be found in other textbooks. The book also contains many original observations or new ways of illustrating even well-known subjects. In fact, the authors wish to convey in this book the sense of wonder in the logical simplicity and at the same time the beauty of subtle and far-reaching consequences of Quantum Mechanics, to young physics students in particular. Problem sets are provided at the end of each chapter, to be solved either analytically or by numerical methods. The solutions to both types of problems are given as separate pdf files or as Mathematica notebooks (there are 88 of them), all together on a CD accompanying the textbook. The presence of such a collection of numerical analyses enriches the main text and is one of the characteristic features of the book. With the many interesting systems discussed, the book will also be a useful reference for researchers and teachers. It provides the reader with a unique, enjoyable and rather complete textbook of Quantum Mechanics, destined to set a new standard for many years to come.
The textbook covers the background theory of various effects discussed from first principles, as clearly as possible, to introduce students to the main ideas of quantum physics and to teach the basic mathematical methods and techniques used in the fields of advanced quantum physics, atomic physics, laser physics, nanotechnology, quantum chemistry, and theoretical mathematics. Many of the predictions of quantum physics appear to be contrary to our intuitive perceptions, and the student will learn how it comes about that microscopic objects (particles) behave in unusual ways that are called quantum effects, what we mean by quantum, and where this idea came from. The textbook is supplemented with Problems and Solutions in Quantum Physics, which contains a wide range of tutorial problems from simple confidence builders to fairly challenging problems that provide adequate understanding of the basic concepts of quantum physics.
Einstein's papers on quantum theory over the period 1905-1925 are reviewed. These papers played a fundamental role in the development of quantum concepts. This review traces the relationship between these papers, on the one hand, and Wien's and Planck's theoretical work on thermal radiation and Einstein's own work on statistical thermodynamics, on the other. Einstein's 1905 development of the concept of light quanta from Wien's radiation law, the application of this concept to elementary interactions of radiation with matter, Einstein's 1906–1907 analysis of the Planck radiation law, and Einstein's development of the foundations of a quantum theory of specific heat are all discussed. Particular attention is paid to Einstein's 1909 development of the concept of a particle-wave duality for radiation from a study of the energy and momentum fluctuations in a radiation field. Einstein's 1916 papers on the quantum theory of radiation are analyzed, and it is emphasized that Einstein was the first to suggest a probabilistic interpretation of the particle-wave duality, in addition to introducing coefficients to characterize the probabilities for optical transitions and offering his well-known derivation of the Planck radiation law. There is a special discussion of Einstein's expression, in his 1925 paper on the quantum theory of monatomic ideal gases, of high regard for de Broglie's concept of a particle-wave duality for material particles.
A lesson series on quantum physics was taught to grade 12 students in 5 different secondary schools. Among others, the series contained a special demonstration experiment for particle-wave duality (double-slit single-photon interference) which was supplemented by the PhET applet quantum wave interference. Preconceptions on particles and waves were assessed in a pretest. Interviews were conducted with 24 students in 4 schools after the demonstration. A posttest was administered to 112 students in 3 schools. Some lessons were observed by an outside observer and/or videotaped, followed by interviews. Results indicate that learning objectives of quantum physics are well within reach of the 12th grade students. This shows especially in student discussions of the PhET applet. However, understanding of wave-particle duality is hindered by insufficient understanding of the prerequisite wave concept that waves are spread out in space. Most students associated a wave with an oscillation and somehow forgot about the spatial aspects. As a consequence, the “strangeness” of wave-particle duality was underappreciated. Also, the link with the de Broglie wavelength discussed early in the lesson series was not made. As in the 5th school quantum physics started several weeks later, we were able to try an improved lesson design for the demonstration successfully. Interviews are very helpful in catching misinterpretations of demonstrations and generating suggestions for improvement. Students do appreciate the confusing wonders of quantum physics but in the post-interviews seem unaware of the many quantum-based devices around them and the many everyday phenomena (like color) which need quantum physics for explanation. Perhaps as teachers and curriculum developers, we are too eager to overemphasize the exotic and strange aspects of quantum theory and underemphasize utility in everyday applications.