ON REFLECTION OF ELECTRONS BY METALLIC CRYSTALS 



889 



penetrate the crystal, and flow away through the remainder of the circuit. 

 We call R the reflection coefficient, and we can define it alternatively as the 

 ratio of the intensity of the reflected electron beam to the intensity of the 

 incident beam. 



We wish to calculate i? as a function of E. In order to be able to do this 

 effectively, it is necessary to idealize the actual physical situation quite 

 drastically. (However, the idealization which we shall use preserves what 

 seem to be the most important features of the physical situation.) On the 

 other hand, once the idealization has been set up, the mathematical calcula- 

 tions themselves will be carried through without approximations^. Hence, 



INCIDENT ELECTRONS 



REFLECTED ELECTRONS 



Fig. 1 — Reflection of an electron beam by a crystal. (Schematic representation). 



any discrepancies between the theoretical results and the results of experi- 

 ment are to be attributed to the inadequacy of the model, and not to il- 

 legitimate steps in the mathematical work. 



Our idealization of the physical situation can be described in the form of 

 the three following assumptions : 



Assumption I. The problem may be treated as one concerning one-dimen- 

 sional motion of electrons. Thus, we set up a rectangular coordinate system 

 in space; and we assume that the crystal occupies the half-space x < 0, 

 and that all of the point functions with which we are concerned depend 

 solely upon the coordinate x. 



Assumption II. There exists a function V{x), such that an electron at the 

 point X has potential energy V{x) ; and the behavior of an electron is gov- 

 erned by the Schrodinger wave equation 



^ Except, of course, simple arithmetical approximations, such as are involved in almost 

 all calculations. 



