CONTEMPORARY ADVANCES IN PHYSICS, XXVIII 



601 



-F 



_i_ 



E/ne 



Fig. 14 — Illustrating an artificial case of a potential-curve with' a single square- 

 topped potential-hill. 



Vm E/ne 



Fig. 15 — Illustrating an artificial case of a potential-curve with a pointed hill. 



1 



E/ne 



Fig. 16 — Illustrating an artificial case of a potential-curve with a valley between 



two hills. 



guessed by the reader — they are constants to which any values may 

 be assigned, and the eventual result of the mathematical operations is 

 going to be taken as referring to a stream of particles of charge ne, 

 mass m and energy E. 



The problem is stated as that of finding a solution of (21) for what- 

 ever value is chosen for E — a solution everywhere single-valued, 

 bounded, continuous, and possessed of a continuous first derivative, 

 such being the general requirement in quantum mechanics. Not, 

 however, any solution possessing these qualities, but a solution apt to 

 the physical situation. On the right of the hill, it must specify a 

 wave-train (I) going from right to left; for we are interested in the 

 adventures of particles coming from the right toward the hill. But 

 on the right of the hill, it must also be capable of specifying a wave- 

 train (II) going from left to right, for some or all of the particles may 

 be reflected from the hillside. On the left of the hill it must be capable 

 of specifying a wave-train (III) going from right to left, for some or 

 all of the particles may traverse the hill and continue on their way. 



