Sttpp lenient to '' Nature,'' July 7, 1923 



39 



of the atom may be resolved and which, according 

 to the classical theory, determine the properties of 

 the radiation to which the motion of the particles 

 gives rise. 



According to the correspondence principle, it is 

 assumed that every transition process between two 

 stationarv states can be co-ordinated with a corre- 



FiG. 6. 



sponding harmonic vibration component in such a 

 way that the probability of the occurrence of the 

 transition is dependent on the amplitude of the vibra- 

 tion. The state of polarisation of the radiation eniitted 

 during the transition depends on the further character- 

 istics of the vibration, in a manner analogous to that 

 in which on the classical theory the intensity and state 

 of polarisation in the wave system emitted by the 

 atom as a consequence of the presence of this vibration 

 component would be determined respectively by the 

 amplitude and further characteristics of the vibration. 



With the aid of the correspondence principle it 

 has been possible to confirm and to extend the above- 

 mentioned results. Thus it was possible to develop a 

 complete quantum theory explanation of the Zeeman 

 effect for the hydrogen lines, which, in spite of the 

 essentially different character of the assumptions that 

 underlie the two theories, is very similar throughout 

 to Lorentz's original explanation based on the classical 

 theory. In the case of the Stark effect, where, on 

 the other hand, the classical theory was completely 

 at a loss, the quantum theory explanation could be 

 so extended with the help of the correspondence 

 principle as to account for the polarisation of the 

 different components into which the lines are split, 

 and also for the characteristic intensity distribution 

 exhibited by the components. This last question has 

 been more closely investigated by Kramers, and the 

 accompanying figure will give some impression of how 

 completely it is possible to account for the phenomenon 

 under consideration. 



Fig. 6 reproduces one of Stark's well-known photo- 

 graphs of the splitting up of the hydrogen lines. The 

 picture displays very well the varied nature of the 

 phenomenon, and shows in how peculiar a fashion the 

 intensity varies from component to component. The 

 components below are polarised perpendicular to the 

 field, while those above are polarised parallel to 

 the field. 



Fig. 7 gives a diagrammatic representation of the 

 experimental and theoretical results for the line Hy, 

 the frequency of which is given by the Balmer 

 formula with n" = 2 and «' — 5. The vertical lines 

 denote the components into which the line is split 



up, of which the picture on the right gives the 

 components which are polarised parallel to the field 

 and that on the left those that are polarised per- 

 pendicular to it. The experimental results are re- 

 presented in the upper half of the diagram, the 

 distances from the dotted line representing the 

 measured displacements of the components, and the 

 lengths of the lines being proportional to the relative 

 intensity as estimated by Stark from the blackening 

 of the photographic plate. In the lower half is given 

 for comparison a representation of the theoretical 

 results from a drawing in Kramers' paper. 



The symbol («',/-«",") attached to the lines gives 

 the transitions between the stationary states of 

 the atom in the electric field by which the com- 

 ponents are emitted. Besides the principal quan- 

 tum integer n, the stationary states are further 

 characterised by a subordinate quantum integer 5, 

 which can be negative as well as positive and has a 

 meaning quite different from that of the quantum 

 number k occurring in the relativity theory of the 

 fine structure of the hydrogen lines, which fixed 

 the form of the electron orbit in the undisturbed 

 atom. Under the influence of the electric field both 

 the form of the orbit and its position undergo 

 large changes, but certain properties of the orbit 

 remain unchanged, and the subordinate quantum 

 number s is connected with these. In Fig. 7 the 

 position of the components corresponds to the fre- 

 quencies calculated for the different transitions, and 

 the lengths of the lines are proportional to the 

 probabilities as calculated on the basis of the corre- 

 spondence principle, by which also the polarisation 

 of the radiation is determined. It is seen that the 

 theory reproduces completely the main feature of 

 the experimental results, and in the fight of the corre- 

 spondence principle we can say that the Stark effect 

 reflects down to the smallest details the action of 

 the electric field on the orbit of the electron in the 

 hydrogen atom, even though in this case the reflection 

 is so distorted that, in contrast with the case of the 

 Zeeman effect, it would scarcely be possible directly 



..ll.l i.ll 



I. ill. I 



I III 



III I 



...I 



11 rrri ii 1 1 I 1 1 ^ m i i m i ii 1 1 1 i 



Fig. 7- 



to recognise the motion on the basis of the classical 

 ideas of the origin of electromagnetic radiation. 



Results of interest were also obtained for the spectra 

 of elements of higher atomic number, the explanation 

 of which in the meantime had made important progress 

 through the work of Sommerfeld, who introduced 

 several quantum numbers for the description of the 



