Quantum Mechanics for Scientists and Engineers

This book introduces quantum mechanics to scientists and engineers. It can be used as a text
for junior undergraduates onwards through to graduate students and professionals. The level
and approach are aimed at anyone with a reasonable scientific or technical background looking
for a solid but accessible introduction to the subject. The coverage and depth are substantial
enough for a first quantum mechanics course for physicists. At the same time, the level of
required background in physics and mathematics has been kept to a minimum to suit those also
from other science and engineering backgrounds.
Quantum mechanics has long been essential for all physicists and in other physical science
subjects such as chemistry. With the growing interest in nanotechnology, quantum mechanics
has recently become increasingly important for an ever-widening range of engineering
disciplines, such as electrical and mechanical engineering, and for subjects such as materials
science that underlie many modern devices. Many physics students also find that they are
increasingly motivated in the subject as the everyday applications become clear.
Non-physicists have a particular problem in finding a suitable introduction to the subject. The
typical physics quantum mechanics course or text deals with many topics that, though
fundamentally interesting, are useful primarily to physicists doing physics; that choice of
topics also means omitting many others that are just as truly quantum mechanics, but have
more practical applications. Too often, the result is that engineers or applied scientists cannot
afford the time or cannot sustain the motivation to follow such a physics-oriented sequence. As
a result, they never have a proper grounding in the subject. Instead, they pick up bits and
pieces in other courses or texts. Learning quantum mechanics in such a piecemeal approach is
especially difficult; the student then never properly confronts the many fundamentally
counterintuitive concepts of the subject. Those concepts need to be understood quite deeply if
the student is ever going to apply the subject with any reliability in any novel situation. Too
often also, even after working hard in a quantum mechanics class, and even after passing the
exams, the student is still left with the depressing feeling that they do not understand the
subject at all.
To address the needs of its broad intended readership, this book differs from most others in
three ways. First, it presumes as little as possible in prior knowledge of physics. Specifically, it
does not presume the advanced classical mechanics (including concepts such as Hamiltonians
and Lagrangians) that is often a prerequisite in physics quantum mechanics texts and courses.
Second, in two background appendices, it summarizes all of the key physics and mathematics
beyond the high-school level that the reader needs to start the subject. Third, it introduces the
quantum mechanics that underlies many important areas of application, including
semiconductor physics, optics, and optoelectronics. Such areas are usually omitted from
quantum mechanics texts, but this book introduces many of the quantum mechanical principles
and models that are exploited in those subjects.
It is also my belief and experience that using quantum mechanics in several different and
practical areas of application removes many of the difficulties in understanding the subject. If
quantum mechanics is only illustrated through examples that are found in the more esoteric
branches of physics, the subject itself can seem irrelevant and obscure. There is nothing like
designing a real device with quantum mechanics to make the subject tangible and meaningful.
Even with its deliberately limited prerequisites and its increased discussion of applications, this
book offers a solid foundation in the subject. That foundation should prepare the reader well
for the quantum mechanics in either advanced physics or in deeper study of practical
applications in other scientific and engineering fields. The emphasis in the book is on
understanding the ideas and techniques of quantum mechanics rather than attempting to cover
all possible examples of their use. A key goal of this book is that the reader should
subsequently be able to pick up texts in a broad range of areas, including, for example,
advanced quantum mechanics for physicists, solid state and semiconductor physics and
devices, optoelectronics, quantum information, and quantum optics, and find they already have
all the necessary basic tools and conceptual background in quantum mechanics to make rapid
progress.
It is possible to teach quantum mechanics in many different ways, though most sequences will
start with Schrödinger’s wave equation and work forward from there. Even though the final
emphasis in this book may be different from some other quantum mechanics courses, I have
deliberately chosen not to take a radical approach here. This is for three reasons: first, most
college and university teachers will be most comfortable with a relatively standard approach
since that is the one they have most probably experienced themselves; second, taking a core
approach that is relatively conventional will make it easier for readers (and teachers) to
connect with the many other good physics quantum mechanics books; third, this book should
also be accessible and useful to professionals who have previously studied quantum mechanics
to some degree, but need to update their knowledge or connect to the modern applications in
engineering or applied sciences.
The background requirements for the reader are relatively modest, and should represent little
problem for students or professionals in engineering, applied sciences, physics, or other
physical sciences. This material has been taught with apparent success to students in applied
physics, electrical engineering, mechanical engineering, materials science, and other science
and engineering disciplines, from 3rd year undergraduate level up to graduate students. In
mathematics, the reader should have a basic knowledge in calculus, complex numbers,
elementary matrix algebra, geometrical vectors, and simple and partial differential equations.
In physics, the reader should be familiar with ordinary Newtonian classical mechanics and
elementary electricity and magnetism. The key requirements are summarized in two
background appendices in case the reader wants to refresh some background knowledge or fill
in gaps. A few other pieces of physics and mathematics are introduced as needed in the main
body of the text. It is helpful if the student has had some prior exposure to elementary modern
physics, such as the ideas of electrons, photons, and the Bohr model of the atom, but no
particular results are presumed here. The necessary parts of Hamiltonian classical mechanics
will be introduced briefly when required in later Chapters.
This book goes deeper into certain subjects, such as the quantum mechanics of light, than most
introductory physics texts. For the later Chapters on the quantum mechanics of light, additional
knowledge of vector calculus and electromagnetism to the level of Maxwell’s equations are
presumed, though again these are summarized in appendices.
One intent of the book is for the student to acquire a strong understanding of the concepts of
quantum mechanics at the level beyond mere mathematical description. As a result, I have
chosen to try to explain concepts with limited use of mathematics wherever possible. With the
ready availability of computers and appropriate software for numerical calculations and
simulations, it is progressively easier to teach principles of quantum mechanics without as
heavy an emphasis on analytical techniques. Such numerical approaches are also closer to the
methods that an engineer will likely use for calculations in real problems anyway, and access
to some form of computer and high-level software package is assumed for some of the
problems. This approach substantially increases the range of problems that can be examined
both for tutorial examples and for applications.
Finally, I will make one personal statement on handling the conceptual difficulties of quantum
mechanics in texts and courses. Some texts are guilty of stating quantum mechanical
postulates, concepts and assumptions as if they should be obvious, or at least obviously
acceptable, when in fact they are far from obvious even to experienced practitioners or
teachers. In many cases, these are subjects of continuing debate at the highest level. I try
throughout to be honest about those concepts and assumptions that are genuinely unclear as to
their obviousness or even correctness. I believe it is a particularly heinous sin to pretend that
some concept should be clear to the student when it is, in fact, not even clear to the professor
(an overused technique that preserves professorial ego at the expense of the student’s!).
It is a pleasure to acknowledge the many teaching assistants who have provided much useful
feedback and correction of my errors in this material as I have taught it at Stanford, including
Aparna Bhatnagar, Julien Boudet, Eleni Diamanti, Onur Fidaner, Martina Gerken, Noah
Helman, Ekin Kocabas, Bianca Nelson, Tomas Sarmiento, and Scott Sharpe. I would like to
thank Ingrid Tarien for much help in preparing many parts of the course material, and Marjorie
Ford for many helpful comments on writing.
I am also pleased to acknowledge my many professorial colleagues at Stanford, including
Steve Harris, Walt Harrison, Jelena Vuckovic, and Yoshi Yamamoto in particular, for many
stimulating, informative, and provocative discussions about quantum mechanics. I would
especially like to thank Jelena Vuckovic, who successfully taught the subject to many students
despite having to use much of this material as a course reader, and who consequently corrected
numerous errors and clarified many points. All remaining errors and shortcomings are, of
course, my sole responsibility, and any further corrections and suggestions are most welcome.