This book is based on graduate courses taught by the author over the last
fourteen years in the mathematics department of Stony Brook University.
The goal of these courses was to introduce second year graduate students
with no prior knowledge of physics to the basic concepts and methods of
quantum mechanics. For the last 50 years quantum physics has been a driv-
ing force behind many dramatic achievements in mathematics, similar to
the role played by classical physics in the seventeenth to nineteenth cen-
turies. Classical physics, especially classical mechanics, was an integral part
of mathematical education up to the early twentieth century, with lecture
courses given by Hilbert and Poincar´e. Surprisingly, quantum physics, es-
pecially quantum mechanics, with its intrinsic beauty and connections with
many branches of mathematics, has never been a part of a graduate math-
ematics curriculum. This course was developed to partially ﬁll this gap and
to make quantum mechanics accessible to graduate students and research
L.D. Faddeev was the ﬁrst to develop a course in quantum mechanics for
undergraduate students specializing in mathematics. From 1968 to 1973 he
regularly lectured in the mathematics department of St. Petersburg State
University in St. Petersburg,
and the author enjoyed the opportu-
nity to take his course. The notes for this book emerged from an attempt to
create a similar course for graduate students, which uses more sophisticated
mathematics and covers a larger variety of topics, including the Feynman
path integral approach to quantum mechanics.
that time in Leningrad, Soviet Union.