This work was first published in 1947 in German under the title "Re-
chenmethoden der Quantentheorie". It was meant to serve a double
purpose: to help both, the student when first confronted with quantum
mechanics and the experimental scientist, who has never before used it
as a tool, to learn how to apply the general theory to practical
problems of atomic physics. Since that early date, many excellent books
have been written introducing into the general framework of the theory
and thus indispensable to a deeper understanding. It seems, however,
that the more practical side has been somewhat neglected, except, of
course, for the flood of special monographs going into broad detail on
rather restricted topics. In other words, an all-round introduction to
the practical use of quantum mechanics seems, so far, not to exist and
may still be helpful. It was in the hope of filling this gap that the
author has fallen in with the publishers' wish to bring the earlier
German editions up to date and to make the work more useful to the
worldwide community of science students and scientists by writing the
new edition in English. From the beginning there could be no doubt that
the work had to be much enlarged. New approximation methods and other
developments, especially in the field of scattering, had to be added. It
seemed necessary to include relativistic quantum mechanics and to offer,
at least, a glimpse of radiation theory as an example of wave field
quantization.
