we are interested in (related to the Lorentz invariance violation present in the theory) are actually due to the change of the spin state of the electron (described by coefficients (\[sol\_coeffs\]) of the wave functions (\[sol\_phi\])), and spin effects should disappear in the classical limit.

General theory
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Consider the electron[^1] transitions from some given initial state $ \Psi $ with energy $ E $ to a lower state $ \Psi' $ with energy $ E' $. Assuming the system of the wave functions is orthonormalized, the total radiation power obtained using the methods of QED (the standard Feynman rules) can be written in the first order of $ e^{2} $ as follows (see, e.g., [@book_qed], and also [@book_rel_el], [@book_hep_rad]; we follow the approach of [@book_rel_el], [@book_hep_rad] while describing the theory of the synchrotron radiation in this section): $$\label{rad_W_def}
    W = \frac{e^{2}}{2\pi} \int d^{3}k \ \delta( E - E' - k ) \, S, \qquad
    S = \left| {\langle}{\boldsymbol}\alpha {\rangle}{\bf f} \right|^{2}.$$ Here $ {\bf k} $ is the wave vector of the photon emitted, so that the energy of the photon is $ \omega = k \equiv |{\bf k}| $; $ {\bf f} $ is the vector characterizing the 