238 THE QUANTUM [xvn. 4 
which is a constant and so disappears when we are considering 
differences of levels. It may be recalled that so-called half 
quantum numbers have been employed for some time in con 
nection with band spectra. 
Fues * * * § has worked out the band theory of diatomic molecules 
in detail, taking into account the mutual influence of rotation 
and oscillation and also the fact that the oscillation is not of the 
simple harmonic type. The result is in exact agreement with 
the ordinary treatment except that the quantum numbers be 
come half-integral also in all correction terms. 
A theory of the Stark effect based on Schrodinger’s ideas has 
been presented by Epstein f who considers the radiation from a 
hydrogen-like atom in an electric field. After a general mathe 
matical exposition of the method, the positions of the components 
are determined to terms of the second order in the electrical field. 
The positions of the lines practically coincide with those obtained 
in Epstein’s old theory which gave excellent agreement with 
experiment. The main interest lies in the expressions for the 
intensities, which are simple in their structure and agree with the 
observed values better than the expressions derived by Kramers 
from Bohr’s correspondence principle. A further point of interest 
is that components which, in the old theory, had to be ruled out 
by a special postulate, now drop out automatically. Schrodinger 
himself has discussed the same problem and obtained similar 
results. 
A generalized operator calculus for dealing with the equations 
of quantum dynamics has been developed by Carl Eckart J, 
who claims that it leads to methods of solution much simpler 
than those previously given. Born and Wiener § had previously 
shown that the matrices were closely related to a special form of 
operator, and that the operator calculus furnished a means of 
calculating the matrices. Eckart shows that the results of 
Schrodinger may be included in the matrix calculus of Born and 
Jordan, thus giving an independent confirmation of Schrodinger’s 
own presentation || (based on his wave-mechanics) of the mathe 
matical equivalence of the two theories. 
An interesting suggestion as to the physical meaning of the 
wave-function ip has been made by Schrodinger. Let ip denote 
a conjugate complex value. Then ipip is the square of the abso 
lute value of the complex function ip and in the case of the 
hydrogen atom is proportional to the charge of the electron, 
* Fues, Ann. d. Physik, vol. 80, p. 367, 1926. 
f Epstein, Phys. Rev., vol. 28, p. 659, 1926. 
J Carl Eckart, Phys. Rev., vol. 28, p. 7x1, 1926. 
§ Born and Wiener, Zeits. f. Physik, vol. 36, p. 174, 1926. 
|| Schrodinger, Ann. d. Physik, vol. 79, p. 734, 1926.