Quantum Mechanics A Modern and Concise Introductory Course

Quantum mechanics is undergoing a revolution. Not that its substance is changing,
but major developments are placing it in the focus of renewed attention, both
within the physics community and among the scientifically interested public. First,
wonderfully clever table-top experiments involving the manipulation of single
photons, atomic particles and molecules are revealing in an ever-more convincing
manner theoretically predicted facts about the counterintuitive and sometimes
“spooky” behavior of quantum systems and have led to a renewed interest in the
formulation of a strictly physics-based (non-philosophical) foundation of quantum
mechanics. Second, the prospect of building quantum computers with enormously
increased capacity of information-processing is developing great interest and high
hopes in the engineering and computer science communities. Third, condensed
matter physics and nanotechnology are narrowing down the gap between classical
and quantum domains in the practical realm. These developments demand more
and better training in quantum mechanics at the universities, with emphasis on a
clear and solid understanding of the subject. Cookbook-style learning of quantum
mechanics, in which equations and methods for their solution are memorized rather
than understood, may help the students to solve some standard problems and pass
multiple-choice tests, but it will not enable them to break new ground in real
life as physicists. On the other hand, some “Mickey Mouse courses” on quantum
mechanics for engineers, biologists and computer analysts may give an idea of what
this discipline is about, but too often the student ends up with an incorrect picture or,
at best, a bunch of uncritical, blind beliefs in linear algebra wizardry. The present
book represents a fresh start toward helping achieve a deep understanding of the
subject. It presents the material with utmost rigor and will require ironclad, old
fashioned discipline from the students in their study.
Too frequently, in today’s universities, we hear the demand that the courses
offered be “entertaining,”in response to which somedepartmentalbrochuresdeclare
that “physics is fun”! Studying physics requires many hours of hard work, deep
concentration, long discussions with buddies, periodic consultation with faculty,
and tough self-discipline. But it can, and should, become a passion: the passion
to achieve a deep understanding of how Nature works. This understanding usually

comes in discrete steps, and students will experience such a step-wise mode of
progress as they work their way diligently throughthe present book.The satisfaction
of having successfully mastered each step will then indeed feel very rewarding!
The “amount of information per unit surface” of text is very high in this book
its pages cover all the important aspects of present-day quantum mechanics, from
the one-dimensional harmonic oscillator to teleportation. Starting from a few basic
principles and concentrating on the fundamental behavior of quantum systems
(particles) with only a few degreesof freedom(low-dimensionHilbert space) allows
the author to plunge right into the core of quantum mechanics. It also makes it
possible to introduce first the Heisenberg matrix approach– in my opinion, a
pedagogically rewarding method that helps sharpen the mental and mathematical
tools needed in this discipline right at the beginning. For instance, solving the
quantization of the harmonic oscillator without the recourse of a differential
equation is illuminating and teaches dexterity in handling the vector and matrix
representation of states and operators, respectively.
Daniel Bes is a child of the Copenhagen school. Honed in one of the cradles of
quantum mechanics by ˚ Age Bohr, son of the great master, and by Ben Mottelson,
he developed an unusually acute understanding of the subject, which after years of
maturing he now has projected into a book– now in its third edition. The emphasis
given throughout the text to the fundamental role and meaning of the measurement
process will help the student overcome the initial reaction to the counterintuitive
aspects of quantum mechanics and better comprehend the physical meaning and
properties of Schr¨ odinger’s wave function. The human brain is an eminently
classical system (albeit the most complex one in the Universe as we know it), whose
phylo-and ontogeneticevolutionare drivenby classical interactionsbetween organ
ism and the environment, and which processes pragmatic information, definable
only in the classical domain.It is therefore only natural that when this classical brain
looks into the microscopic domain, using human-designed instruments which must
translate quantum happenings into classical, microscopically observable effects,
strange things with unfamiliar behavior may appear in our mental images! And it is
only natural that, thus, the observer’s way of thinking and instruments should not be
left completely outside the fundamental framework of quantum physics! Bes’ book
helps to recognize, understand and accept quantum “paradoxes” not as such but as
the facts of “Nature under human observation.” Once this acceptance has settled in
the mind, the student will have developed a true intuition or, as the author likes to
call it, a “feeling” for quantum mechanics.
Chapter 2 contains the real foundation on which quantum mechanics is built;
it thus deserves, in my opinion, repeated readings– not just at the beginning
but after each subsequent chapter. With the exception of the discussion of two
additional principles, the rest of the book describes the mathematical formulations
of quantum mechanics (both the Heisenberg matrix mechanics, most suitable for
the treatment of low-dimension state vectors, and Schr¨ odinger’s wave mechanics
for continuous variables) as well as many up-to-date applications. The examples
cover a wide variety of topics, from the simple harmonic oscillator mentioned
abovetosubjects in condensedmatterphysics,nuclearphysics,electrodynamicsand

quantum computing. It is interesting to note, regarding the latter, that the concept of
qubit appears in a most natural way in the middle of the book, almost in passing,
well before the essence of quantum computing is discussed towards the end. Of
particular help are the carefully thought-out problems at the end of each chapter, as
well as the occasional listings of “commonmisconceptions.”A mostwelcometouch
is the inclusion of a final chapter on the history of theoretical quantum mechanics
indeed, it is regrettable that so little attention is given to it in university physics
curricula: much additional understanding can be gained from learning how ideas
have matured (or failed) during the historical development of a given discipline!
Let me conclude with a personal note. I have known Daniel Bes for almost
70 years. As a matter of fact, I had known of him even before we met in person:
our fathers were “commuter–train acquaintances” in Buenos Aires, and both served
on the PTA of the primary school that Daniel and I attended (in different grades).
Daniel and I were physics students at the University of Buenos Aires (again,
at different levels), then on the physics faculty, and years later, visiting staff
membersofLosAlamosNationalLaboratory.Wealwayswerefriends,but we never
worked together– Daniel was a theoretician almost from the beginning, whereas
I started as a cosmic-ray and elementary-particle experimentalist (see Fig.2.7).
Interestingly, reading the first edition of this book has motivated me a few years
ago to expand my current interest in foundations of information theory and work
towards developing yet another interpretation of quantum mechanics (which I call
“information-based”)!
It gives me a particular pleasure that after so many decades and despite residing
at opposite ends of the American continent, we have become professionally
“entangled” through this wonderful textbook