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Physics Education

Gradual introduction of some aspects of quantum mechanics in a high school curriculum

CUPPARI A., G. Rinaudo, Ornella Robutti, Paolo Violino

Published Sep 1, 1997• 40 citations
Publisher

Abstract

The basic concepts of quantum mechanics can be introduced at a high school level by considering the action of classical mechanics and then introducing Planck's constant as the granularity of that action. A practical example of the periodic motion of a spring allows students to investigate the limits of classical mechanics, and concepts such as the Uncertainty Principle can be discussed.

DOI
10.1088/0031-9120/32/5/012

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The basic concepts of quantum mechanics can be introduced at a high school level by considering the action of classical mechanics and then introducing Planck's constant as the granularity of that action. A practical example of the periodic motion of a spring allows students to investigate the limits of classical mechanics, and concepts such as the Uncertainty Principle can be discussed.
Quantum Mechanics is being included in numerous school programmes as part of the curriculum. Most modern textbooks introduce it emphasising its strange or, at least uncommon, somewhat paradoxical, character. We argue that such an approach is wrong because rather than attracting the interest of students toward the topic, it makes quantum mechanics almost unbelievable and artificial. The resulting perception is that quantum mechanics is in fact not understood at all and that we need a new theory that eventually will supersede it. In contrast, we propose a new approach on classical physics that, stressing the role of the measurements in physics, introduces the concept of state very early in the curriculum. Such a concept is reviewed on each classical physics topic and the concept of force as a vector is almost abandoned for the concept of interaction defined as something that change the state. In this way it is possible to introduce quantum mechanics without violating any conviction the students acquired learning classical physics. In other words quantum mechanics appears to be as natural as classical physics, at least from the point of view of the results of the experiments.
It is now generally accepted that quantum mechanics occupies a central place in microscopic physical theory. The importance of this discipline shows up in the research journals, and also in the graduate physics curriculum. Not only is quantum mechanics a required subject, both for experimental and theoretical students; it appears as well to be influencing the way in which classical physics is taught. Presentations of classical mechanics that slight the traditional problems of planetary motion, unsymmetrical tops and dissipative systems in favor of collision theory and Poisson brackets are becoming more and more prevalent. With the much younger subject of classical electrodynamics, the analogous tendency is less marked, although here again emphasis is being placed on those examples that bring the student closest to the formalism of quantum electrodynamics. Such trends are of course proper and reasonable, especially so long as no important classical ideas are omitted from consideration. Indeed, the study of acoustics, hydrodynamics, and elasticity probably benefits from an early introduction of field concepts.
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We present an approach for teaching quantum physics at high school level based on the simplest quantum system - the single quantum bit (qubit). We show that many central concepts of quantum mechanics, including the superposition principle, the stochastic behavior and state change under measurements as well as the Heisenberg uncertainty principle can be understood using simple mathematics, and can be illustrated using catchy visualizations. We discuss abstract features of a qubit in general, and consider possible physical realizations as well as various applications, e.g. in quantum cryptography.
`Quantum Mechanics'' is a comprehensive introduction to quantum mechanics for advanced undergraduate students in physics. It provides the reader with a strong conceptual background in the subject, extensive experience with the necessary mathematical background, as well as numerous visualizations of quantum concepts and phenomena. - ;Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples is a comprehensive introduction to non-relativistic quantum mechanics for advanced undergraduate students in physics and related fields. It provides students with a strong conceptual background in the most important theoretical aspects of quantum mechanics, extensive experience with the mathematical tools required to solve problems, the opportunity to use quantum ideas to confront modern experimental. realizations of quantum systems, and numerous visualizations of quantum concepts and phenomena. Changes from the First Edition include many new discussions of modern quantum systems (such as Bose-Einstein condensates, the quantum Hall effect, and wave packet revivals) all in the context of familiar. textbook level examples. The book continues to emphasize the many connections to classical mechanics and wave physics to help students use their existing intuition to better learn new quantum concepts. -