CONTEMPORARY ADVANCES IN PHYSICS 



681 



strings. It is important to realize this. Schroedinger's way of think- 

 ing provides not a single atom-model for each sort of atom, but as 

 many distinct models as there are Stationary States.* 



n=0 



Fig. 2 (after Schroedinger). 



Interpretation of the Hydrogen Atom by Wave- Mechanics 

 The hydrogen atom is conceived as a system endowed with the 

 potential energy V = — e^/r. This form for the potential energy, 

 I recall, is obtained by imagining an electron and a nucleus, or more 

 precisely two point-charges + e and — e, separated by a distance 

 denoted by r. The image of the electron and the nucleus does not 

 come over explicitly into the new theory; but in spirit it does come 

 over, for the potential-energy-function derived from that image is the 

 basis for the new theory. 



Polar coordinates for the wave-equation are imperiously suggested 

 by a potential-energy-function of this form, and consequently it is 

 thus expressed : 



2m {E + e-jr) 



V-'^ = 



df^ 



and putting Ejh for the vibration-frequency, we attain 



V2^ + 



sivm 



li' 



£ + 



^ = 0. 



(172) 



The resemblance of these equations to those laid down for the ball 

 of fluid is as unmistakable as the resemblance of the wave-equation 

 for a linear oscillator to that of a stretched string. Here we have 

 the case of a fluid in which the wave-speed varies from point to point, 

 according to the law 



«2 = £2/2m(£ -f eVr), (173) 



* Some may find satisfaction in conceiving, as my colleague Dr. T. C. Fry sug- 

 gests, a "string" so constructed that the speed of propagation of waves along it is a 

 function of their frequency. 



