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Quantum spin-flip transitions are of great importance in the synchrotron radiation (SR) theory. For better understanding of the nature of this phenomenon, it is necessary to except the effects connected with the electric charge radiation from observation. This fact explains the suggested choice of the spin-flip radiation model in the form of radiation of the electric neutral Dirac-Pauli particle moving in the homogeneous magnetic field. It is known that in this case, the total radiation in the quantum theory is conditioned by spin-flip transitions. The idea is that spin-flip radiation is represented as a nonstationary process connected with spin precession. From this point of view, we shall shown how to construct a solution of the classical equation of spin precession in the BMT theory having the exact solution of the Dirac-Pauli equation. Thus, one will find the connection of the quantum spin-flip transitions with classical spin precession.According to the uncertainty principle, for the spin-flip transition with the characteristic frequency of SR [1] we obtainwhere µ is the magnetic moment, ρ is the radius of curvature of the relativistic electron trajectory in the homogeneous magnetic field H. The ratio of the transition time ∆t and the time of the radiation forming ∆t on the circular arc dl ≈ γρ is equal ∆t/∆t ≈ 2πγ −4 ≪ 1.That means that in the ultrarelativistic case, spin-flip transitions are practically noninertial, that is why the electron motion can be considered for the time ∆t as uniform and rectilinear.Let us consider the electric neutral Dirac-Pauli particle, which moves in the homogeneous magnetic field H = (0, 0, H). As is known [2], wave function of the above particle has the form Ψ(r, t) = L −3/2

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