700 BELL SYSTEM TECHNICAL JOURNAL 



placement of charge; and in the spectra, the Hnes which such tran- 

 sitions should cause are missing. 



Thus in the case of the hydrogen atom exposed to an electric field, 

 and in other two- and three-dimensional systems as well, the identifica- 

 tion of the square of the amplitude of the ^-vibrations with density of 

 electric charge is thrice successful. In the picture, we see the electric 

 charge stationary when the system is in a stationary state, fluctuating 

 with the proper frequency when two states coexist ; we see it surging 

 back and forth en masse when the coexisting states are two between 

 which a transition is "permitted," and otherwise not; we see it 

 surging back and forth along the proper direction to explain the polari- 

 zation of the light which results from the transition. As a device for 

 picturing the radiation-process, Schroedinger's model is certainly un- 

 rivalled. In the earlier atom-models, even the frequencies of the 

 emitted rays of light and the frequencies of the intra-atomic vibrations 

 did not agree. Here at last they do, and when a tube full of hydrogen 

 atoms is pouring out the light of the red Balmer line with its frequency 

 of 4.57-10^^, it is permissible at last to imagine each of them as a 

 mechanism, within which something is vibrating 4.57-10^^ times in 

 a second. 



Even the relative intensities of spectrum lines may fall within the 

 scope of wave-mechanics. We have seen that in the case of the linear 

 oscillator, the vanishing of the integral J'xfifjdx for all pairs of Sta- 

 tionary States for which i and j difTer by more than one unit entails 

 the non-occurrence of the corresponding transitions, the inability to 

 emit or absorb the corresponding radiation. May it not be that the 

 intensity of the radiation emitted by reason of the transition between 

 any two states of any system, and polarized parallel to any direction 

 X, is governed by the value of the integral Sxypi^^jdx involving the 

 Eigenjunktionen 4'% and ^j of the states in question? To develop this 

 idea more assumptions must be introduced than I have yet mentioned, 

 since every Eigenfunktion which I have thus far written down might 

 be multiplied by any constant factor without ceasing to be an Eigen- 

 funktion, and some rule must be laid down to fix these constant 

 factors. To predict the relative intensities of the components into 

 which certain hydrogen-atom lines are split by electric field, Schroe- 

 dinger made a simple and natural assumption about these factors; and 

 the results turned out to be in good agreement with the data.'"^ I 

 cannot enter further into this topic, except to remark that the point 

 of contact between wave-mechanics and the matrix-mechanics ot 

 Heisenberg lies here; for the integrals in question figure as matrix- 



30 Schroedinger, /1mm. d. Phys., 80, pp. 464-478 (1926); Phys. Rev. (2), 28, pp. 

 1049-1070 (1926). 



