360 



76 



quantum theory by Ehrenfest^), plays an important part. From Bohr's paper it 

 will, however, be seen that if the undisturbed system is degenerate, i. e. if the 

 number of degrees of freedom is larger than the number of the conditions which 

 fix the stationary states of the undisturbed system, complications present themselves 

 owing to the circumstance that in such a case the stationary states of the perturbed 

 system in general will be fixed by a larger number of conditions. In such a case 

 a closer examination of the motion of the perturbed system, and especially a con- 

 sideration of the small new frequencies, impressed on the motion of the system by 

 the perturbing forces, is necessary in order to obtain a fixation of the stationary 

 states. A general exposition of the methods, developed by Bohr, by means of 

 which it is possible to fix the stationary states of a perturbed system, will be given 

 in the later paper referred to above; in the present case, where we consider the 

 influence of a weak homogeneous electric field on the hydrogen atom, which will 

 not essentially disturb the character of the motion of the atom, we shall only 

 mention the points which have direct connection with this problem, without entering 

 more closely on a theoretical discussion. 



The properties of the mechanical motion of the electron in a hydrogen atom 

 which is exposed to a small electric field of force have been investigated in detail 

 in § 4. From the calculations in this section it is seen that the character of this 

 motion, with neglect of small quantities proportional to the square of the intensity 

 of the perturbing force, may be considered as characterised by three quantities 

 I'-l, 11 and 1!,. If the intensity of the perturbing force is zero (F=-Q), and II -f- /IJ 

 coincide with the quantities /j and /, respectively, which in the notation of § 2 char- 

 acterise the motion of the electron in the undisturbed atom. The quantity 7° represents 

 2 - times the angular momentum of the electron round an axis through the nucleus 

 parallel to the electric force. While the stationary states of the undisturbed atom, 

 which forms a degenerate system, are fixed by the two conditions (117), the statio- 

 nary states of the perturbed system will, disregarding small quantities proportional 

 to F\ be characterised by the following three conditions: 



= n, h, n = {n., — n) h , /;' = ii/i , (124) 



where /ij, and n are positive integers of which n^>\\. A state of the perturbed 

 system satisfying these conditions for given values of yjj, n.^, \\ will in the follow- 

 ing be characterised by the symbol {n^, n.^\ u). Comparing with the formulae in 

 ,^ 4, it is seen from (124) that the motion in a stationary state of the perturbed 

 system will, at any moment, only differ by small quantities proportional to the 

 intensity F of the perturbing force from a stationary motion of the undisturbed 

 system, which besides satisfying the conditions (117) satisfies the additional condi- 

 tion that the angular momentum of the electron round the axis is equal to an 

 entire multiple of ''/2;r. It will be seen that the latter condition fixes the position 

 of the plane in which the electron moves, which was naturally left undetermined 



') See Bohr, Ioc. eit. Part I, p. 8. 



