220 BELL SYSTEM TECHNICAL JOURNAL 



If we are required by these recent developments to accept quanta 

 as actual particles which carry the energy and momentum of light, 

 how, in terms of such particles, are we to explain interference? How 

 are we possibly to get on without waves? We even depend upon the 

 waves to supply us with information concerning the energy and 

 momentum of the quanta. One way in which it has been proposed to 

 resolve the difficulty is to relegate the waves to the comparatively 

 unimportant role of supplying the laws of motion of the quanta. Let 

 us assume, for example, that when a stream of quanta passes through a 

 narrow slit the particles do not continue in straight lines as Newton 

 supposed, but that they spread out in such a fashion that the current 

 density of quanta proceeding in different directions is proportional to 

 the intensity of the light proceeding in these directions as calculated 

 on the wave theory. In making this assumption we have given over 

 classical mechanics and explained diffraction — or at least described 

 it — by setting up a form of wave mechanics in its place. 



With this rather crude and incomplete picture before us of light 

 quanta being guided in their motion by waves, it is not difficult to 

 imagine the general trend of de Broglie's speculations, de Broglie 

 sensed that electrons like quanta might have waves to guide them — to 

 supply the laws of their motion. That the ordinary laws of mechanics 

 are adequate to describe the motions of electrons in discharge tubes is 

 not inconsistent with this view, for it is well known that these laws 

 are adequate also for a corpuscular theory of light to within the 

 accuracy with which the phenomena are described by geometrical 

 optics. It is only when one tries to explain diffraction that the simple 

 corpuscular theory fails him. de Broglie envisaged a similar situation 

 in regard to electrons — a range of small scale phenomena requiring a 

 wave theory for their proper description. Assuming the frequency of 

 these hypothetical waves to be given by the total energy of the electron 

 divided by h, de Broglie was able to show that the length of the waves 

 would be given by h divided by the momentum of the electron^ — and 

 this as it happens is just the relation which obtains between the wave- 

 length and momentum of quanta. 



The goal toward which de Broglie was striving, as I have mentioned, 

 was a new theory of the atom, and he was able to point at once to a 

 suggestive relationship which exists between the lengths of these 

 hypothetical electron-waves and the lengths of the circular orbits in 

 the Bohr atom. The permitted orbits are just those which contain 

 an integral number of these electron wave-lengths. But it was 

 Schroedinger, as we all know, who elaborated these ideas into a 

 comprehensive wave theory of mechanics, and showed the tremendous 



