In this paper we present a proposal for teaching basic aspects of quantum mechanics in high school. Our proposal is based on a wave approach that makes use of the analogies between wave phenomena at macroscopic scales and phenomena at atomic or subatomic scales. Although the classical and the quantum model are completely different, there is a common underlying wave mathematical layer. This allows to address, via analogies, quantum aspects that are not accessible to direct experience. The quantization of energy levels, the quantum interference and the uncertainty relations are examples of quantum aspects having an analog concept in classical physics wave phenomena. In our approach we break the wave-particle “duality”, which is totally counterintuitive. Instead we enhance the underlying wave mathematical structure as a path to reach and explain emerging features of particles and quantum systems in general.
In this paper we present a proposal for teaching basic aspects of quantum mechanics in high school. Our proposal is based on a wave approach that makes use of the analogies between wave phenomena at macroscopic scales and phenomena at atomic or subatomic scales. Although the classical and the quantum model are completely different, there is a common underlying wave mathematical layer. This allows to address, via analogies, quantum aspects that are not accessible to direct experience. The quantization of energy levels, the quantum interference and the uncertainty relations are examples of quantum aspects having an analog concept in classical physics wave phenomena. In our approach we break the wave-particle “duality”, which is totally counterintuitive. Instead we enhance the underlying wave mathematical structure as a path to reach and explain emerging features of particles and quantum systems in general.
Abstract Wave-particle duality is included in many secondary school and university physics curricula as a concept central to quantum physics. The very term wave-particle duality suggests that a firm grasp of the individual classical concepts of wave and particle is crucial to studying quantum mechanics successfully. This raises the question whether students’ mental models of these concepts are sufficiently addressed and developed prior to the teaching of wave-particle duality. We explored Dutch upper secondary school students’ mental models of waves and particles using a short questionnaire. It was administered to a total of 147 students from two different groups. One group consisted of secondary school students prior to receiving formal education in introductory quantum mechanics while students from the other group had recently completed the Dutch national curriculum for pre-university education, which includes wave-particle duality. Our findings support the notion that students model classical particles and waves as mutually exclusive phenomena. Mental models of wave-particle duality, which require mixing the two classical models, appear to be only superficially developed. Our findings open avenues for future research on students’ mental models of waves and particles as basis for wave-particle duality.
The most important basic aspect of Quantum Mechanics description is the wave, but there are many different interpretations between different schools and scientists about the reality of this wave. Till now there are more than thirteen important schools of interpretation for the basic concepts of quantum mechanics. In the case of the wave, some interpretations consider it as a real wave, while others consider it as only a mathematics toll. Through our experience in teaching quantum theory, we conclude that teaching quantum mechanics is not only just deriving beautiful and maybe logical equations and relations related to the subject. We believe that each step of deriving those equations or relations should be followed by deep discussions of concepts and meanings. Because of the students difficulty for understand the wave concept as an example of general basic concepts of quantum mechanics. For this purpose and in order to clarify and focus on the problematic, a questionnaire sheet was presented to homogenous sample of Algerian third year physics students related to the subject. But we concluded from the results of students’ survey, that the basic concepts of quantum mechanics should have a profound educational revision.
The combination of mathematical and conceptual difficulties makes teaching quantum physics at secondary schools a precarious undertaking. With many of the conceptual difficulties being unavoidable, simplifying the mathematics becomes top priority. The particle/wave-in-a-box provides a teaching model which includes many aspects of serious quantum physics, while avoiding most of the mathematics. In a Dutch quantum physics project for secondary schools, this model was adopted to play a key role. Much to our surprise, we ran into many more applications than we originally expected. In many instances the model yields order of magnitude estimates, for instance of atomic and nuclear size, or qualitative insights, for instance about energy levels, molecular bonding and electron pressure. Moreover, either directly or with minor modifications, the particle-in-a-box model provides reasonable approximations of a range of phenomena, including the absorption spectra of organic pigments, the mass of the proton and the spectra of quantum dots.
Introduction The evolution of microelectronics toward reduced device sizes has proceeded to a degree that renders conventional models, approaches, and theories inapplicable. Indeed, for objects with sizes of 100 nanometers or less it is frequently the case that the length scales associated with fundamental physical processes are comparable to the geometrical size of the device; also, fundamental time scales associated with physical processes are of the order of the time parameters for nanodevice operation. Therefore, on the nanoscale the theories and models underlying modern nanoelectronics become more complicated, and rely more and more on basic science. Generally, in the nanoworld the fundamental laws of physics that govern particles and material fields differ from those that apply to familiar macroscopic phenomena such as the motion of a baseball or a train. Instead of classical mechanics, that works so well for macroscopic phenomena, the motion of particles in the nanoworld is determined by the so-called wave mechanics or quantum mechanics. An underlying principle of central importance for nanophysics is the fundamental concept that all matter , including electrons, nuclei, and electromagnetic fields, behaves as both waves and particles , that is, wave–particle duality is a basic characteristic of all matter. At first glance, wave properties and particle properties for the same physical object are hardly compatible. To understand wave–particle duality, we will briefly review, in the following two subsections, the basic properties of particles and waves known from classical physics.
Abstract The Einstein-First project approaches the teaching of Einsteinian physics through the use of physical models and analogies. This paper presents an approach to the teaching of quantum physics which begins by emphasising the particle-nature of light through the use of toy projectiles to represent photons. This allows key concepts including the spacing between photons, and photon momentum to be introduced. This in-turn allows an intuitive understanding of the uncertainty principle. We present optical interference in the context of individual photons, using actual videos showing the development of images one at a time. This enables simple laser interference experiments to be interpreted through the statistical arrival of photons. The wave aspects of quantum phenomenon are interpreted in terms of the wavelike nature of the arrival probabilities.
Introduction to the Maths and Physics of Quantum Mechanics details the mathematics and physics that are needed to learn the principles of quantum mechanics. It provides an accessible treatment of how to use quantum mechanics and why it is so successful in explaining natural phenomena. This book clarifies various aspects of quantum physics such as ‘why quantum mechanics equations contain “I”, the imaginary number?’, ‘Is it possible to make a transition from classical mechanics to quantum physics without using postulates?’ and ‘What is the origin of the uncertainty principle?’. A significant proportion of discussion is dedicated to the issue of why the wave function must be complex to properly describe our “real” world. The book also addresses the different formulations of quantum mechanics. A relatively simple introductory treatment is given for the “standard” Heisenberg matrix formulation and Schrodinger wave-function formulation and Feynman path integrals and second quantization are then discussed. This book will appeal to first- and second-year university students in physics, mathematics, engineering and other sciences studying quantum mechanics who will find material and clarifications not easily found in other textbooks. It will also appeal to self-taught readers with a genuine interest in modern physics who are willing to examine the mathematics and physics in a simple but rigorous way. Key Features: Written in an engaging and approachable manner, with fully explained mathematics and physics concepts Suitable as a companion to all introductory quantum mechanics textbooks Accessible to a general audience