Connecting different concepts is very important in bringing new perspectives to established principles and is often related to lateral thinking. Lateral thinking often provides old contents with interesting new light that motivates students to become more effective in exploring chemical knowledge and understanding. The usefulness of lateral thinking is here demonstrated by three aspects of traditional quantum mechanics in which we provide original thoughts in traditional fields.
Connecting different concepts is very important in bringing new perspectives to established principles and is often related to lateral thinking. Lateral thinking often provides old contents with interesting new light that motivates students to become more effective in exploring chemical knowledge and understanding. The usefulness of lateral thinking is here demonstrated by three aspects of traditional quantum mechanics in which we provide original thoughts in traditional fields.
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.
The more science tells us about the world, the stranger it looks. Ever since physics first penetrated the atom, early in this century, what it found there has stood as a radical and unanswered challenge to many of our most cherished conceptions of nature. It has literally been called into question since then whether or not there are always objective matters of fact about the whereabouts of subatomic particles, or about the locations of tables and chairs, or even about the very contents of our thoughts. A new kind of uncertainty has become a principle of science. This book is an original and provocative investigation of that challenge, as well as a novel attempt at writing about science in a style that is simultaneously elementary and deep. It is a lucid and self-contained introduction to the foundations of quantum mechanics, accessible to anyone with a high school mathematics education, and at the same time a rigorous discussion of the most important recent advances in our understanding of that subject, some of which are due to the author himself.
Quantum mechanics has brought revolutionary changes in the conceptual foundations of physics and continues to shape the modern world. In this book, the author's emphasis is on helping students comprehend the significance of the underlying principles and understand the ways the new concepts were introduced. Including many worked examples and problems, this book will be an invaluable resource for students in physics, chemistry and electrical engineering needing a clear and rigorous introduction to quantum mechanics.
In this paper, we present a new minimal mathematical conceptual approach to quantum mechanics using light polarization for lower secondary school students with the aim of bringing students closer to the so-called quantum mechanical way of thinking. We investigated how students think about some of the basic concepts and fundamental laws and we found that certain concepts are quite well-understandable in younger grades too. We studied the introduction of the so-called state circle, which can faithfully represent quantum mechanical formalism without involving students in abstract algebraic calculations. We then categorized and analyzed students’ thoughts on the superposition principle and the lack of trajectory, finding that the concept of measurement and the lack of trajectory were problematic. We explored that younger students tend to hold gestalt-like mental models of quantum concepts, while at the same time being able to use visualizations correctly for reasoning in the quantum realm. Overall, this paper provides evidence in favor of introducing basic features of quantum mechanics as early as in lower secondary school.
Christian Forstner Quantenmechanik im Kalten Krieg: David Bohm und Richard Feynman ( Stuttgart , GNT-Verlag , 2007 ), 242 pp. , [ hbk ] €30.00 ISBN 978-3-928186-81-0 . This book is about the social context of the development of quantum physics in the Cold War period. It is presented in the form of a comparative socio-biographical study of two American physicists, David Bohm (1917–1993) and Richard Feynman (1918–1988), and their very different careers and approaches and contributions to quantum physics. Bohm is known for his formulation of a new interpretation of quantum mechanics in 1952 invoking so-called ‘hidden parameters'. A year before that, he was suspended from Princeton University because of his involvement with the political Left and took up a position in Brazil. Feynman has often been portrayed, not least by himself, as a completely context-free genius who received the Nobel Prize in 1965 for his contributions to quantum electrodynamics. Forstner offers a fresh view of these theoretical physicists, and what is particularly notable is that not only the ‘outsider’ Bohm but also the ‘genius’ Feynman is placed within a social and ideological context. The book fascinates all the way from its introductory chapter about the emergence of what was (after WWII) called the Copenhagen Interpretation of quantum mechanics and its pragmatic reception in the US (a chapter which perhaps ought to have been called ‘Von Europa nach Amerika’ rather than ‘Von Deutschland nach Amerika’), to the later case studies of Bohm and Feynman and their respective contributions to quantum physics. Unlike the typical numbers-oriented American physicist that focused exclusively on practical calculations, Bohm was preoccupied with the foundations of quantum mechanics and the philosophy of science. Of particular interest is Forstner's analysis of Bohm's early political engagement, his Marxism, and his motivation in dialectical materialism in writing his textbook Quantum Theory (1951) (in which Bohm seems to have been supportive in his own way of the Copenhagen Interpretation), and later in formulating his hidden variables interpretation. In his treatment of Feynman, Forstner analyses and challenges Feynman's self-understanding and demonstrates convincingly that Feynman was not context-free but was driven by an identifiable instrumentalist scientific ideology which, however, contrary to Bohm's, resonated well with the typical American physicist's way of thinking. In his analysis Forstner makes use of Ludwik Fleck's concepts of thought collective and thought style. Hence, the careers of the two main figures and their respective approaches and contributions to quantum physics are understood in relation to their respective local and political thought collectives and thought styles. Through this perspective social aspects of the development of theoretical physics become obvious. However, sometimes the use of Fleck's scheme seems to get in the way of the flow of the narrative, and it fails to bring out perspectives of the story pertaining to individual efforts. For example, Forstner explains the fact that Bohm pursued his ideas about a new interpretation of quantum mechanics by his dismissal from Princeton and his later exile from the US, and hence his isolation from the American physicists' thought collective and style; the reason being that Bohm no longer felt inhibited by the American pragmatic thought style but could pursue his own thinking freely. Framing this work in dialectical materialism could even be taken as suggesting it was means of defiance against his oppressors. Indeed this sounds plausible. However, the discussion with Einstein, who was based at the Institute of Advanced Study in Princeton, about the new interpretation of quantum mechanics, seems also to have been important for Bohm's further pursuit of these ideas, and it would have been interesting if this link had been explored on a deeper level. Moreover, the comparative biographical analysis might have been enriched by a greater attention to personal or psychological traits of the two physicists, such as Feynman's humorous attitude and recklessness versus Bohm's tendency to depression. The book has a clear and well balanced structure and Forstner is lucid in addressing the central issues he wants to highlight in the difficult and complex physics of the two protagonists, employing only a few relevant mathematical formulas. The book is based on a wide variety of sources such as original contributions to quantum electrodynamics and the foundations of quantum mechanics, unpublished manuscripts, private correspondence, oral history, and the FBI files about his two heroes.
Quantum mechanics — central not only to physics, but also to chemistry, materials science, and other fields — is notoriously abstract and difficult. This book is a concise, explanatory book that focuses on the fundamental structure, concepts, and methods of quantum mechanics, filling the gap between introductory and advanced studies, between popularizations and technical treatises. Although physical understanding is emphasized, the mathematical sophistication necessary to achieve that understanding is also developed. A modern perspective is adopted throughout, the goal being to gain entry into quantum mechanics as used by practicing scientists. This perspective includes a focus on quantum states generally, not just wavefunctions, and a strong emphasis on Dirac notation. Many standard topics are developed, such as the Schrödinger equation, quantum states, operators, and matrix mechanics. Some non-standard topics are also discussed, such as the complex nature of quantum states, and various interpretations of the uncertainty relations. Discussion of applications is limited, and focuses on elucidating the structure of quantum mechanics.