CHAPTER XVII 
THE NEW QUANTUM MECHANICS 
It is to be hoped that a new era of mutual stimulation of mechanics 
and mathematics has commenced. To the physicists it will at first 
seem deplorable that in atomic problems we have apparently met 
with such a limitation of our usual means of visualization. This 
regret will, however, have to give way to thankfulness that mathe 
matics, in this field too, presents us with the tools to prepare the 
way for further progress. 
Niels Bohr, Nature, December 5, 1925 
1. The Work of Heisenberg 
I N the nineteenth century classical electrodynamic theory had 
considerable success in explaining many of the phenomena 
of atomic physics, but other facts emerged which seemed to 
necessitate a radical departure from this theory. During the first 
quarter of the present century many attempts were made to 
meet these difficulties by means of special assumptions and rules, 
which constituted the quantum theory. Although these methods 
have had remarkable success in the interpretation of a restricted 
set of phenomena, it has long been felt that such a procedure, 
designedly adopted with a particular end in view, was not satis 
factory and that a more general theory was required. 
In 1925 Heisenberg * put forward a new theory of quantum 
mechanics which has had far-reaching consequences, and seems 
to point the way to a complete solution of the problem from the 
mathematical standpoint. One of the fundamental ideas 
employed by Heisenberg is that only such things as are directly 
open to observation should enter into the mathematical formula 
tion. He considered it advantageous to avoid every concept 
which cannot be connected with experiment, and so eliminated 
all ideas of motion within the atom. We are unable to assign 
to an electron a special position in space at a special instant of 
time, so that, as far as our observations are concerned, an electron 
orbit does not exist. In attempting to build up a new quantum 
mechanics in which relations between observable magnitudes 
* Heisenberg, Zeits. f. Physik, voi. 33, p. 879, 1925. 
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