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.
