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Electronics and Power

Why quantum mechanics?

P.A. Lindsay

Published Jan 1, 1968• 0 citations
Publisher

Abstract

It has become fashionable to say that all electrical engineers, or at least those specialising in communication engineering, ought to be familiar with the basic ideas of quantum mechanics. In view of the ever-increasing load of university teaching, is this statement justified, and, if so, why? A reasonable case for the teaching of quantum mechanics to engineers can be made, and some simple ideas and mental analogies can be developed which may prove to be of use to electrical engineers.

DOI
10.1049/ep.1968.0249

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It has become fashionable to say that all electrical engineers, or at least those specialising in communication engineering, ought to be familiar with the basic ideas of quantum mechanics. In view of the ever-increasing load of university teaching, is this statement justified, and, if so, why? A reasonable case for the teaching of quantum mechanics to engineers can be made, and some simple ideas and mental analogies can be developed which may prove to be of use to electrical engineers.
Most engineers need a basic understanding of quantum mechanics, and for this the typical college introduction is enough. Such an introduction tends to be axiomatic but physically unenlightening. The rules of quantum mechanics (QM) are a fait accompli; justified because they work. This is a good beginning, but those needing to learn more face a special quantum barrier: more advanced texts often continue in the axiomatic tradition. Infinite-dimensional spaces, amplitude vectors, matrices, and operators in lieu of momentum and energy-these and other concepts may be introduced with little rationalization or intuition. To an inquiring student, QM can quickly become bizarre; something to be manipulated but not understood. This need not be so. Here the authors present one teaching solution. They show that many of QM's key ideas can be reasoned out from just a few physical assumptions with mathematics that is low in dimension, linear and accessible to many. Some results include a simple reason for believing probability amplitudes are more natural to use than probabilities, the duality of functions as vectors and vice versa, an example of how a matrix, an operator and a physical value might be related, the Heisenberg uncertainty principle and Schrodinger's equation.
There are two ways to teach quantum mechanics. The first way – which for most physicists today is still the only way – follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then, you learn about the “blackbody paradox” and various strange experimental results, and the great crisis these things posed for physics. Next, you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study, you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex. Look, obviously the physicists had their reasons for teaching quantum mechanics that way, and it works great for a certain kind of student. But the “historical” approach also has disadvantages, which in the quantum information age are becoming increasingly apparent. For example, I’ve had experts in quantum field theory – people who've spent years calculating path integrals of mind-boggling complexity – ask me to explain the Bell inequality to them , or other simple conceptual things like Grover's algorithm. I felt as if Andrew Wiles had asked me to explain the Pythagorean Theorem.
We introduce here an approach that presents the basics of quantum mechanics to electrical engineers using common matrix algebra and Fourier series knowledge. Designed to quickly impart a fundamental understanding, this strategy bypasses the complex mathematics typically required. Amidst the unfolding second quantum revolution, the accelerated development of quantum engineering in academia and industry underscores the urgent need for a skilled workforce. Scientific and technological fields like quantum computing, quantum sensing, and quantum communications are gaining significant momentum, necessitating the urgent involvement of electrical engineers skilled in management, design, manufacturing, and research. These professionals require foundational quantum mechanics knowledge to effectively integrate these principles with their existing technical skills in areas like automatic control theory and signal processing. Traditionally, educational methods have targeted physicists rather than engineers, often treating quantum mechanics as too abstract for practical engineering applications. However, the rise of quantum technology now demands the inclusion of engineers from diverse backgrounds. Our proposal offers this primer as an innovative, electrical engineering-focused educational tool. We strongly believe that our approach prepares engineers to make significant contributions to the rapidly expanding field of quantum technology.
Quantum mechanics has evolved from a subject of study in pure physics to one with a wide range of applications in many diverse fields. The basic concepts of quantum mechanics are explained in this book in a concise and easy-to-read manner, leading toward applications in solid-state electronics and optics. Following a logical sequence, the book focuses on key ideas and is conceptually and mathematically self-contained. The fundamental principles of quantum mechanics are illustrated by showing their application to systems such as the hydrogen atom, multi-electron ions and atoms, the formation of simple organic molecules and crystalline solids of practical importance. It leads on from these basic concepts to discuss some of the most significant applications in semiconductor electronics and optics. Containing many homework problems, the book is suitable for senior-level undergraduate and graduate-level students in electrical engineering, material sciences, applied physics and chemistry.