The Absorption of Radiation by Multiply Periodic Orbits, and its Relation to the Correspondence Principle and the Rayleigh-Jeans Law. Part I. Some Extensions of the Correspondence Principle

This part deals with the quantum theory aspects of the problem. In the absence of external radiation fields the distortion in the shape of the orbit is essentially the same in both the classical and quantum theories provided in the former we retain only one particular term ${\tau }_1$, ${\tau }_2$, ${\tau }_3$ in the multiple Fourier expansion of the force $\frac{2e^2\ddot{v}}{3c^3}$ on the electron due to its own radiation. The term to be retained is, of course, the combination overtone asymptotically connected to the particular quantum transition under consideration. Then the changes $\Delta J_1$, $\Delta J_2$, $\Delta J_3$ in the momenta $J_k$ which fix the orbits and which in the stationary states satisfy the relations $J_k=n_{k}h$, are in the ratios of the integers ${\tau }_1$, ${\tau }_2$, ${\tau }_3$ in both the classical and quantum theories, making the character of the distortion the same in both even though the speed of the alterations may differ. One particular term in the classical radiation force is thus competent to bring an orbit from one stationary state to another.