82 



where P represents the total angular momentum of the system round the axis, 

 taken in the same direction as that of the superposed rotation. 



From these results it follows that the motion of the electron in any stationary 

 state of a hydrogen atom, which is exposed to a homogeneous magnetic 

 field, will — if we look apart from small quantities proportional to the square 

 of the intensity of the magnetic force and to the product of this intensity with the 

 ratio between the mass of the electron and that of the nucleus — differ from the 

 motion in some stationary state of the atom in the absence of the field, only by 

 a superposed uniform rotation round an axis through the nucleus parallel to the 

 magnetic force with a frequency given by (79). Due to the degenerate character of 

 the system formed by the atom in the absence of the magnetic field, it is not pos- 

 sible, however, from a consideration of the mechanical effect produced on the 

 motion of the electron by a slow and uniform establishment of the magnetic field, 

 to fix the stationary states of the perturbed atom completely, but in order to fix 

 these states we must consider more closely the relation between the additional 

 energy of the system due to the presence of the magnetic field and the character 

 of the secular perturbations produced by this field on the orbit of the electron. 

 On the basis of Larmor's theorem the discussion of this problem is very simple. 

 In fact, since the frequency Oh is independent of the shape and position of the 

 orbit, we may proceed in a manner which is completely analogous to that applied 

 in the fixation of the stationary states of the hydrogen atom in the presence of a 

 homogeneous electric field. Thus, looking apart from the effect of the relativity 

 modifications, we may conclude at once that the total energy in the stationary 

 states of the atom will be given by 



E = £„ + uoh/i, (80) 



where n is an entire number which can be positive as well as negative, while £„ 

 will be equal to the energy in the corresponding stationary state of the undis- 

 turbed atom, which is given by — W„ in (41). As in the case of the Stark effect, 

 it will moreover be seen that this formula includes the values of the energy in 

 such states of the atom, in which the electron moves in a circular orbit perpendic- 

 ular to the direction of the field, and which beforehand must be expected to be 

 included among the stationary states of the perturbed system, since such orbits 

 during a slow and uniform establishment of the external field will not undergo 

 secular perturbations as regards shape and position (compare page 73). In fact, 

 since in these cases we have P ^ + "^i27z, where n is the entire number character- 

 ising the' stationary states of the undisturbed hydrogen atom, it follows from the 

 above that the total energy in the special stationary states under consideration will 

 just be represented by the formula (80), if we put n = ^ n. From this formula it 

 will be seen at the same time, that the presence of the external magnetic field im- 

 poses the restriction on the motion in the stationary states of the hydrogen atom, 

 that, with neglect of small quantities proportional to H, the angular momentum 



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