the coefficients (\[sol\_coeffs\]), on the mixing angle $ \delta $.

Synchrotron radiation {#rad}
=====================

In this section, we investigate the electromagnetic radiation of an electron moving in a magnetic field using the wave functions obtained earlier. The radiation is handled at the entirely quantum level, in contrast to the classical approach adopted in most of the present-day publications on the similar subject (see, e.g., [@Altschul], [@Montemayor_Urrutia], [@Ellis_Mavromatos_Sakharov]). We shall calculate the asymptotic expressions for the spectral-angular distribution of the one-photon radiation of a high-energy electron in the weak-field limit. Unlike Schwinger’s method that takes only the first quantum corrections into account [@Schwinger_sr], we use the technique that provides us with [*all*]{} the quantum corrections arising. In this respect, our results are [*exact*]{} (i.e., we do not actually make any expansion in powers of $ \hbar $), although they are [*asymptotic*]{}, appropriate for the case of the weak magnetic field $ H \ll H_{c} $ (with respect to Schwinger’s critical field $ H_{c} \simeq 4.41 \cdot 10^{13} \, \text{gauss} $), with the small parameter being the ratio of the mass of the electron to its energy.

It is essential to consider the radiation phenomena at the quantum level, since the effects 