CONTEMPORARY ADVANCES IN PHYSICS 699 



tionary states, the distribution of "charge" along the imaginary string 

 which represents it is stationary; when the vibrations corresponding 

 to two distinct Stationary States coexist, the distribution of the 

 "charge" fluctuates, with precisely the frequency which experiment 

 teaches us to expect from a transition between the states in question ; 

 when and only when the two coexisting stationary states are adjacent 

 in the ordering, when and only when experiment teaches us to expect 

 transitions, the fluctuation assumes the emphatic character of a bodily 

 surging of the charge to and fro across the centre of the string.-^ 



One further desirable result of identifying square of amplitude of ^ 

 with density of electric charge appears when from one dimension we 

 go over to systems of two or three dimensions. As illustration I take 

 the example of an hydrogen atom exposed to an electric field, repre- 

 sented by an imaginary fluid in three dimensions, the stationary wave- 

 patterns of which correspond to the stationary states of the perturbed 

 atom. If two of these stationary wave-patterns coexist, there may 

 be a bodily surging of charge to and fro, with the frequency belonging 

 to the transition between the stationary states which the wave-patterns 

 represent. If in particular two wave-patterns sharing a common 

 value of the quantum-number 5 (the "equatorial quantum-number," 

 equation 186) coexist, there is a surging of the "charge," and its to- 

 and-fro motion is parallel to the applied electric field; there is no 

 component of the motion normal to the field. With this result agrees 

 well the fact of experience, that the light emitted by virtue of transi- 

 tions between stationary states difTering only in the quantum-numbers 

 ki and ki, and sharing the same value of s, is polarized with its electric 

 vector parallel to the field. Again, if two wave-patterns for which the 

 values of 5 differ by one unit coexist, the resultant surging of the 

 charge is perpendicular to the electric field; and it is a fact of ex- 

 perience that the light due to transitions between stationary states 

 having values of s one unit apart is polarized with electric vector nor- 

 mal to the field. Finally, if two wave-patterns for which the values 

 of 5 differ by two or more units coexist, there is no far-sweeping dis- 



"' Schroedinger lias shown that if we conceive a great niimlxT of Stationary 

 States with high values of i and artfully chosen relative "amplitudes" (i.e. values 

 of Ai and Bi in erjuation 201) to exist simultaneously, we find the "charge-density" 

 concentrated into a small region, a sort of knot or bundle which oscillates back and 

 forth across the centre of the string with freciucncy Po and with approximately the 

 same amplitude of vibration as the original particle (the particle with mass ni and 

 restoring- force — Aw-mvo-x of which the string is our image in wave-mechanics) 

 would have if its energy were the same as that of the Stationary- State which was 

 made most prominent in the summation {Naturwiss., 14, pp. 664-666; 1926). This 

 is a promising result, suggesting as it does that atoms in highly excited states may 

 be groups of particles which, as the system returns to normalcy, spread out into a 

 sort of fluid haze. The idea can be generalized widely, and merits a thorough 

 analysis. 



