Abstract
Based on the structure of the energy levels of a relativistic electron moving in a uniform magnetic field first derived by Schneider, a more rigorous quantum theory of gyrotron radiation is developed. As the result, a difference-differential equation is obtained to describe the evolution of gyrotron radiation. This equation is of the form of the spherical Raman-Nath equation, well known in the quantum theory of free-electron lasers. Therefore, all the mathematical techniques developed for solving the spherical Raman-Nath equation can be used immediately to solve the problem of gyrotron radiation.
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