First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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Library of Congress Control Number: 2019950855
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-501-5
Founded in 1925 and 1926 by Werner Heisenberg, Erwin Schrödinger and Paul Dirac, quantum mechanics is nearly 100 years old. As the basis of modern technology, it has given rise to countless applications in physics, chemistry and even biology. The relevant literature is very rich, counting works written in many languages and from various perspectives. They address a broad audience, from beginner students and teachers to expert researchers in the field.
Professor Sakho has chosen the former as the target audience of this book, connecting the quarter of a century that preceded the inception of quantum mechanics and its first results. The book is organized in two volumes. The first deals with thermal radiation and the experimental facts that led to the quantization of matter. The second volume focuses on the Schrödinger equation and its applications, Hermitian operators and Dirac notations.
The clear and detailed presentation of the notions introduced in this book reveals its constant didactic concern. A unique selling point of this book is the broad range of approaches used throughout its chapters:
The book concludes with a list of references and a detailed index.
Science is a key element of contemporary culture. Researchers’ efforts to write the books required for students’ education are praiseworthy. Undergraduate students and teachers will find this work especially beneficial. We wish it a wide distribution.
Louis MARCHILDON
Professor Emeritus of Physics
University of Quebec at Trois-Rivières
July 2019
Quantum mechanics or the physics of the infinitely small (microcosm) is often contrasted with classical mechanics or the physics of macroscopic bodies (macrocosm). This book, whose title is “Introduction to Quantum Mechanics 2”, aims to equip the reader with basic tools that are essential for a good understanding of the physical properties of atoms, nuclei, molecules, lasers, solid bodies and electronic materials – in short all that is infinitely small. Introductory courses on quantum mechanics generally focus on the study of the interaction between matter and radiation, and the quantum states of matter. This book emphasizes the various experiments that have led to the discovery within the set of physical phenomena related to the properties of quantum systems. Consequently, this book is composed of seven chapters organized in two volumes. Each chapter starts with a presentation of the general objective, followed by a list of specific objectives, and finally by a list of prerequisites essential for a good understanding of the concepts introduced. Furthermore, the introduction of each law follows a simple application. Each studied chapter ends with a collection of various rich exercises and solutions that facilitate the assimilation of all the concepts presented. Moreover, a brief biography of each of the thinkers having contributed to the discovery of the studied physical laws or phenomena is given separately, as the chapter unfolds. The reader can this way acquire a sound scientific culture related to the evolution of scientific thought during the elaboration of quantum mechanics. Due to its structuring and didactic approach, this work is a modern and very original book. Volume 1 covers the study of the first four chapters related to thermal radiation, to the experimental facts that revealed the quantization of matter, and to De Broglie wave theory and Heisenberg’s uncertainty principle.
Volume 2 is dedicated to the last three chapters related, respectively, to the study of Schrödinger equation and applications, Hermitian operators and Dirac notations.
Chapter 1 focuses on the study of the evolution of wave functions described by the Schrödinger equation followed by several applications that introduce, in particular, concepts such as potential well, potential path, wave reflection and transmission factor, potential barrier, tunnel effect and 0D confinement through the study of quantum dots. Chapter 2 deals with the basic tools related to the mathematical formalism of quantum mechanics. Hence, this chapter presents the properties of orthonormal bases in the space of square-summable wave functions, Dirac notations for ket and bra vectors in the state space. Moreover, it introduces notions such as linear operator, Hermitian operator, observable, Hermitian conjugation and commutator. Finally, Chapter 3 studies the eigenvalues and eigenvectors of an observable. This offers the possibility to introduce the notion of representation of ket and bra vectors and operators, to pass from vector calculus in the space of square-summable wave functions and to matrix calculus in the space of states. Furthermore, the study relates to the introduction of the eigenvalue equation of an operator and the characteristic equation (or secular equation) for determining the eigenvalues of an operator based on a matrix representation. The chapter ends with the definition of the mean value of an observable and the establishment of their evolution equation by the study of conservative systems, and the establishment of Ehrenfest theorem reflected by the laws of evolution of the mean values of position and momentum operators.
Finally, the book is completed by a set of appendices that offer the reader the possibility to gain a deeper understanding of the physical phenomena studied in this book. Appendices 1 and 2 relate, respectively, to the description of quantum wires, quantum wells and quantum dots of semiconductor materials. This description facilitates the connection with potential wells and potential dots studied in quantum mechanics. Moreover, these appendices make it possible to introduce the notions of 2D, 1D and 0D confinement. Finally, Appendix 3 focuses on the detailed proof of the expression of the transparency of a potential barrier of height V0 for a particle of energy E > V0. This facilitates the introduction of the resonance phenomenon. A list of references and an index can be found at the end of the book.
I wish to thank Chrono Environement Laboratory at the Université Franche Comté de Besançon for their hospitality during my stay from September 1 to November 2, 2018 as a Visiting Professor. Many pages of this book were written during this period, which proved very favorable to this endeavor, both in terms of logistics and documentation. I would like to make a special mention to Jean-Emmanuel Groetz, Senior Lecturer at Chrono Environnement Laboratory, who was in charge of my Visiting Professor request file. I wish to express my warmest thanks to Elie Belorizky, Professor of Physics at Université Joseph Fourier de Grenoble (France), for his critical remarks and suggestions, which had a great contribution to improving the scientific quality of this work. Many corrections brought to this book have been made via telephone exchanges during my stay at the Université Franche
Comté de Besançon. I am expressing here my deep appreciation for him gracefully bearing the inherent expenses for the telephone calls related to this book review. Finally, I wish to address my deepest gratitude to Louis Marchildon, Professor of Physics (Emeritus) at the Université de Quebec à Trois Rivières (Canada), who spared no effort to review the entire book, and whose comments have enhanced the scientific quality of this work, whose foreword bears his signature. We started our collaboration in 2013, when he invited me to host a conference at the Hydrogen Research Institute (HRI). I am deeply grateful for his kind and very fruitful collaboration.
All human endeavor being subject to improvement, I remain open to and interested in critical remarks and suggestions that my readers can send me at the below-mentioned email.
Ibrahima SAKHO
aminafatima_sakho@yahoo.fr
October 2019