Emission of radiation from a nonrelativistic electron in a standing electromagnetic wave field

Expressions are derived for the spectral intensity of the spontaneous radiation and for the gain of a probe wave used to study the interaction between a nonrelativistic electron beam and a standing electromagnetic wave field. Estimates of the frequency and the corresponding gain indicate that an infrared electromagnetic wave may be amplified in the system under study. A criterion that the amplification of the probe wave is a quantum process is derived.