xvii. 4] THE NEW QUANTUM MECHANICS 239 
which is to be regarded not as concentrated in a point but as 
spread throughout space. As the wave-function y> practically 
vanishes not far from the nucleus, the charge is actually restricted 
to a domain of, say, a few Angstroms. It is possible to extend 
this idea to the more general case of several electrons. Thus the 
wave-function physically means and determines a continuous 
distribution of electricity in space, the fluctuations of which 
determine the radiation by the laws of ordinary electrodynamics. 
Further evidence in favour of the connection between the 
field scalar ip and the electric density of the current has been 
given by Fermi.* * * § He has shown that Schrödinger’s hypothesis 
leads to the right expression for the magnetic moment of a 
hydrogen-like atom. He considers only the part of the magnetic 
moment which, in the old quantum theory, was supposed to be 
due to the orbital motion of the electron, leaving the magnetic 
moment of the spinning electron to be considered separately. 
The wave equation for a hydrogen-like atom in a magnetic 
field has been integrated by Fock,f and it appears from his 
solution that the lines of current are circles situated in planes 
perpendicular to the axis and with their centres on the axis. 
It is hence shown that the component of the magnetic moment 
in the direction of the field is the product of a Bohr magneton 
and the magnetic quantum number of the old theory. It is 
noteworthy that this magnetic moment arises in a certain way 
through the action of the field in which the atom is situated. 
In view of this result it seems safe to infer that the number 
of quantum magnetic tubes of induction associated with the 
atom in this state is equal to the magnetic quantum number. 
It is of interest to find that there appears to be a possibility 
of correlating wave mechanics with Maxwell’s theory. This 
question has been discussed by Bateman,| de Broglie,§ and 
Carrelli. || Functions can be found satisfying the wave equation 
and giving for the electric and magnetic fields the values char 
acteristic of an electric pole of assigned charge. It is also possible 
to introduce the spinning electron into the theory, and obtain 
expressions for the electric and magnetic fields due to a spinning 
charge which is equivalent as regards the magnetic field to a 
magnetic dipole. 
We have referred in Chapter XI to the five-dimensional theory 
of Kaluza and Klein. The relation of this theory to the 
undulatory mechanics of Schrödinger has been discussed by Klein 
* Fermi, Nature, vol. 118, p. 876, 1926. 
f Fock, Zeits. f. Physik, vol. 38, p. 242, 1926. 
X Bateman, Nature, vol. 118, p. 839, 1926. 
§ de Broglie, C.R., vol. 184, p. 81, 1927. 
|| Carrelli, Nature, vol. 119, p. 492, 1927.