Electron Wave Optics 17 



A=— (12) 



tnv 



and this de Broglie wavelength fits also well into the relativistic 

 scheme. 



De Broglie started very far ofif, in a very general way ; it is 

 therefore not surprising that he failed to point out the concrete 

 physical significance of these waves which Einstein was the first 

 to recognize. Stimulated by Einstein's hints, E. Schrodinger, in 

 1925, approached the subject afresh from a new angle. Starting 

 from the Hamiltonian analogy, he established the equation for 

 the propagation of de Broglie's waves in electro-magnetic fields 

 by that combination of deduction and guessing wdiich is indis- 

 pensable for every great physical discovery. ^^ He showed that 

 by means of his wave equation the older quantum theory, which 

 up to then was a collection of somewhat arbitrary looking rules, 

 not always in agreement with experiments, could be put on a 

 solid and general basis which explained even those features of 

 atomic and molecular spectra where the older theory failed. The 

 direct experimental evidence, however, for the de Broglie waves 

 was still outstanding. As early as 1925, W. Elsasser suggested 

 that certain curious features in the reflection pattern of electrons 

 on nickel crystals may be due to de Broglie waves. Fully con- 

 vincing proof w^as obtained, in 1927, by Davisson and Germer, 

 and almost simultaneously by G. P. Thomson. ^^ 



It was known since von Laue's discovery, in 1912, that crystal- 

 line bodies (for instance metals), in which the elementary con- 

 stituents, ions, atoms, or molecules, are arranged in lattices of 

 high regularity, can serve as a sort of diffraction grating for 

 X-rays, as the spacing in these lattices is usually of the same 

 order as the wavelength of X-rays which is equal to or larger 

 than 



12^40 

 V 



A, = ^^— A 



if V is the potential in volts which was used to accelerate the 

 electrons which produced the X-rays. 



