in a coordinate-free way, and makes it straightforward to move to the chosen
coordinate system once that has been identified. Moreover, Dirac’s notation
brings into sharp focus the still mysterious concept of a probability ampli-
tude. Hence, it is important to introduce Dirac’s notation from the outset,
and to use it for an extensive discussion of probability amplitudes and why
they lead to qualitatively new phenomena.

x
Preface
In the winter of 2008/9 the book was used as the basis for the second-
year introductory quantum-mechanics course in Oxford Physics. At the out-
set there was a whiff of panic in the air, emanating from tutors as well as
students.
Gradually more and more participants grasped what was going
on and appreciated the intellectual excitement of the subject. Although the
final feedback covered the full gamut of opinion from “incomprehensible” to
“the best course ever” there were clear indications that many students and
some tutors had risen to the challenge and gained a deeper understanding of
this difficult subject than was previously usual. Several changes to the text
of this second edition were made in response to feedback from students and
tutors. It was clear that students needed to be given more time to come to
terms with quantum amplitudes and Dirac notation. To this end some work
on spin-half systems and polarised light has been introduced to Chapter 1.
The students found orbital angular momentum hard, and the way this is
handled in what is now Chapter 7 has been changed.
The major changes from the first edition are unconnected with our ex-
perience with the 2008/9 course: principally Chapter 6 is now a new chapter
on composite systems.
It starts with material transferred from the end of
Chapter 2 of the first edition, but quickly moves on to a discussion of en-
tanglement, the Einstein–Podolski–Rosen experiment and Bell inequalities.
Sections on quantum computing, density operators, thermodynamics and the
measurement problem follow. It is most unusual for the sixth chapter of a
second-year textbook to be able to take students to the frontier of human un-
derstanding, as this chapter does. Moreover, the section on thermodynamics
makes it possible to add thermodynamics to the applications of the adiabatic
principle discussed in Chapter 11. More minor changes include the addition
of a section on the Heisenberg picture to Chapter 4, and the correction of a
widespread misunderstanding about the singlet-triplet splitting in helium.
Problem solving is the key to learning physics and most chapters are
followed by a long list of problems. These lists have been extensively revised
since the first edition and printed solutions prepared. The solutions to starred
problems, which are mostly more-challenging problems, are now available
online
1
and solutions to other problems are available on request to colleagues
who are teaching a course from the book.

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