The theory of spontaneous emission by electrons during their motion along the quantizing magnetic field of a star

The quantum motion of non-relativistic and relativistic electrons in the presence of constant magnetic fields at the surfaces of magnetic stars, magnetic white dwarfs, and pulsars is considered. The quantizing magnetic-field strengths for charged particles with specified energies are determined. The quantum motion of these particles in a plane perpendicular to the magnetic field is accompanied by spontaneous radiation due to electron transitions from higher to lower discrete energy levels, right down to the ground state. In the non-relativistic case, this emission is monochromatic. In the non-relativistic case, various frequencies are emitted, but lie within an order of magnitude of each other. The electron kinetic energy along the magnetic field varies from zero to a maximum value, due to the one-dimensional character of the motion along the field, between each pair of potential barriers corresponding to the discrete energy levels. The results may be relevant to describing gamma-ray flares of pulsars.