58 
QUANTUM THEORY 
wellian stresses; thus the energy and momentum led into any material 
system is computed and the observable response of the system is indicated. 
Here the quantum theory makes a change. According to it the Poynting 
vector does not measure the flux of energy but the probability of a flux. 
Considering a surface where the energy is passing into or out of a material 
system the flux can only occur in complete quanta; and where the classical 
theory gives a flux of a fraction p of a quantum, the quantum theory gives 
a probability p of the flux of a whole quantum. 
The reasons for this view are very strong. Firstly, it leaves the wave 
theory of propagation of light in vacuum entirely undisturbed; interference 
bands will appear where the undulatory theory predicts. At the same time 
the energy units are preserved from weakening by spreading, because it 
is not the energy which is spread by the waves but a state of the aether 
which measures the probability of a jump of energy. Secondly, it modifies 
the classical theory at a point where the classical theory was already 
obscure. One of the still outstanding problems of the relativity theory is 
why a particular tensor formed from F should represent energy, 
momentum and stress; because (so to speak) the tensor does not look like 
energy, momentum and stress and no investigation has been able to make 
the connection appear unartificial. According to the quantum view the 
tensor measures a probability and is not the actual energy-tensor of the 
field. Thirdly, it accounts for the absence of quantisation of free radiation 
implied in the postulates of Einstein’s equation; and it agrees with the 
Correspondence Principle that the classical formulae represent the limit 
when large numbers of quanta are involved, since for large numbers the 
probabilities become equivalent to averages. 
None the less, the progress thus made is quite rudimentary, and if this 
key opens one door it is only to reveal other firmly locked doors ahead. 
Quantisation of the Hydrogen Atom. 
42. Consider a nucleus of charge Ze attended by a single electron of 
mass m and charge — e which describes a Keplerian ellipse around it. The 
mass of the nucleus is regarded as infinitely great compared with m. 
The acceleration of the electron is Ze 2 /mr 2 so that the motion is under 
a central acceleration p,/r 2 , where 
/x = Ze 2 [m (42-1). 
The position of the electron may be described by the canonical variables 
of Delaunay’s planetary theory, viz. 
q 1 = l 0 -w, q 2 = w - Q, q 3 = Q. 
p 1 = m([xa)^, p 2 = m (¡¿a)^ (1 — e 2 )~, p 3 — m (p,a)- (1 — e 2 )^ cos i 
(42-2),