CHAPTER 3 

 ELECTRON WAVE OPTICS 



UP to here, we have considered electrons as charged par- 

 ticles and, following Hamilton, established the analogy of 

 their trajectories with the light rays of geometrical optics. 

 It is well known that the concept of a ray of light is of limited 

 validity, applicable only as long as the physical apertures in the 

 optical system are very large in comparison with the wavelength. 

 It is one of the greatest discoveries of modern physics that the 

 idea of electron trajectory is subject to quite similar restrictions. 

 The bold idea of associating a wave with the motion of a 

 particle emerged first in the head of Louis de Broglie, in 1924. 

 By using the theory of relativity, this immensely powerful tool 

 for physical discoveries, de Broglie could show that from the 

 data of an electron in motion it is possible to define the data of 

 a wave in such a way that their association is relativistically in- 

 variant, which in modern physics is equivalent to saying that 

 it might have physical sense. He took a further step by combin- 

 ing this result with the other great source of modern physics, 

 quantum theory. Classical physics is continuity physics, one 

 physical datum in it is as good as any other. The only distin- 

 guished datum, ''constant of nature/' which occurs in it, is the 

 velocity of light ; but no com1)ination of c with the dynamical data 

 of the particle, i.e., its mass ni, and its velocity v, will give a 

 length, therefore, as far as classical theory goes, the wavelength 

 of these hypothetical waves could be just anything. Quantum 

 theory, however, gives a new universal constant, the natural unit 

 of action h ^ 6.54 X 10"^^ erg/sec. The dimension of action can 

 be also written momentum X length. A zvavelengtJi associated 

 with the motion could be therefore defined as follows ; 



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