x Preface

book and from von Neumann’s classical book, Mathematical Founda-

tions of Quantum Mechanics.

The approach to the construction of quantum mechanics adopted

in these lectures is based on the assertion that quantum and classi-

cal mechanics are different realizations of one and the same abstract

mathematical structure. The features of this structure are explained

in the first few sections, which are devoted to classical mechanics.

These sections are an integral part of the course and should not be

skipped over, all the more so because there is hardly any overlap of

the material in them with the material in a course of theoretical me-

chanics. As a logical conclusion of our approach to the construction

of quantum mechanics, we have a section devoted to the interconnec-

tion of quantum and classical mechanics and to the passage to the

limit from quantum mechanics to classical mechanics.

In the selection of the material in the sections devoted to appli-

cations of quantum mechanics we have tried to single out questions

connected with the formulation of interesting mathematical problems.

Much attention here is given to problems connected with the theory

of group representations and to mathematical questions in the theory

of scattering. In other respects the selection of material corresponds

to traditional textbooks on general questions in quantum mechanics,

for example, the books of V.A. Fok or P.A.M. Dirac.

The authors are grateful to V.M. Babich, who read through the

manuscript and made a number of valuable comments.

L.D. Faddeev and O.A. Yakubovski˘ı