The Radiation of a High Energy Electron in a Constant Magnetic Field

The quantum-mechanical radiation formula for an electron in a constant magnetic field—rigorous within the approximation of the first power of the fine structure constant—is derived. With it, the quantum effects for energies $E_{\mathrm{Bev}}<4\left(\frac{{10}^4}{H_{\mathrm{gauss}}}\right)$ are analyzed and their importance assessed. The electron and the photon severally are subject to fluctuations which produce effects that are quite significant relative to the difference between the velocity of light and that of the electron, the decisive quantity at high energies. The net result however is that they are inconsequential in the domain investigated and that in its radiative aspects the system behaves—for all practical purposes—classically.