This textbook is a detailed survey of a course of lectures given in
the Mathematics-Mechanics Department of Leningrad University for
mathematics students. The program of the course in quantum me-
chanics was developed by the first author, who taught the course from
1968 to 1973. Subsequently the course was taught by the second au-
thor. It has certainly changed somewhat over these years, but its goal
remains the same: to give an exposition of quantum mechanics from
a point of view closer to that of a mathematics student than is com-
mon in the physics literature. We take into account that the students
do not study general physics. In a course intended for mathemati-
cians, we have naturally aimed for a more rigorous presentation than
usual of the mathematical questions in quantum mechanics, but not
for full mathematical rigor, since a precise exposition of a number of
questions would require a course of substantially greater scope.
In the literature available in Russian, there is only one book
pursuing the same goal, and that is the American mathematician
G.W. Mackey’s book, Mathematical Foundations of Quantum Me-
chanics. The present lectures differ essentially from Mackey’s book
both in the method of presentation of the bases of quantum mechan-
ics and in the selection of material. Moreover, these lectures assume
somewhat less in the way of mathematical preparation of the stu-
dents. Nevertheless, we have borrowed much both from Mackey’s
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