Preface

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

mathematicians.

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,

Russia1,

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.

1At

that time in Leningrad, Soviet Union.

xiii

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

mathematicians.

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,

Russia1,

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.

1At

that time in Leningrad, Soviet Union.

xiii