[§3. General Considerations continued.]
We shall now return to the discussion (see [p. 7]) of the special assumptions used in deducing the expressions (3) on [p. 5] for the stationary states of a system consisting of an electron rotating round a nucleus.
For one, we have assumed that the different stationary states correspond to an emission of a different number of energy-quanta. Considering systems in which the frequency is a function of the energy, this assumption, however, may be regarded as improbable; for as soon as one quantum is sent out the frequency is altered. We shall now see that we can leave the assumption used and still retain the equation (2) on [p. 5], and thereby the formal analogy with Planck’s theory.
Firstly, it will be observed that it has not been necessary, in order to account for the law of the spectra by help of the expressions (3) for the stationary states, to assume that in any case a radiation is sent out corresponding to more than a single energy-quantum,
. Further information on the frequency of the radiation may be obtained by comparing calculations of the energy radiation in the region of slow vibrations based on the above assumptions with calculations based on the ordinary mechanics. As is known, calculations on the latter basis are in agreement with experiments on the energy radiation in the named region.
Let us assume that the ratio between the total amount of energy emitted and the frequency of revolution of the electron for the different stationary states is given by the equation
, instead of by the equation (2). Proceeding in the same way as above, we get in this case instead of (3)
