WAVES AND CORPUSCLES HE BROGLIE 251 



But we meet with two cases where the hiws of chisjsical mechanics 

 fail to predict the movements of the corpuscle as will the new theory. 

 The first case is where the propairation of the associated wave is 

 limited to a region of space of which tlie dimensions are of the 

 order of magnitude of the wave length. This occurs for an electron 

 in the interior of an atom. The wave associated witli the atom is 

 then obliged to take the form of a stationary wave analogous to the 

 elastic stationary waves which may occur in a cord fixed at both 

 ends or the stationary electric waves which form in the antennae 

 used for wireless telegraphy. Theory shows that these stationary 

 waves can take only certain well-defined wave lengths corresponding 

 to certain definite movements of the associated electron. These move- 

 ments are precisely the quantized states introduced by Bohr in his 

 theory of the atom and we now have an explanation of the hitherto 

 very mysterious fact that these quantized states are the only possible 

 ones for an electron bound to an atom. 



There is a second case where the movement of the electrons, ac- 

 cording to the laws of the new mechanics, should not obey the laws 

 of the classical mechanics. This is where the associated waves strike 

 an obstacle in the path of propagation. Interference phenomena are 

 then produced and the movements of the associated corpuscles are no 

 longer what would be expected from the classical mechanics. In 

 order to render an account of what takes place, let us be guided by 

 an analogy with radiations. Let us imagine tliat we observe a radia- 

 tion of known wave length with a contrivance capable of showing 

 interference upon a screen. Since we know that the radiations are 

 formed of photons, we can just as well say that we see a swarm of 

 photons upon the screen. In this conception, in the places where in- 

 terference takes place, the photons arrange themselves in such a 

 manner that they become concentrated where the light intensities are 

 the greatest. If we now send upon the same screen, not a radiation 

 but a bundle of electrons of which the associated waves have the same 

 wave length as the radiation previously employed, the waves will 

 interfere in the same manner as in the preceding case since it is this 

 wave length which controls the phenomena of interference. It is 

 therefore quite natural to suppose that the electrons are concentrated 

 there where the intensity is the greatest; in other words, in the new 

 experiment the electrons arrange them.«elves in space similarly as did 

 the photons in the first experiment. If we can prove that this is 

 indeed the case we would then have shown the existence of a wave 

 associated with an electron and we could measure its wave length, 

 establi.shing the truth of the fundamental basis of wave mechanics. 



Now, wave mechanics leads us to attribute to electrons moving 

 with such speeds as usually occur in our experiments, an associated 

 wave whose wave length is of the order of that of X rays (0,0001 



