We consider a problem of electron motion in different media and magnetic field. It is shown that in case of nonmoving medium and constant homogenious magnetic field the electron energies are quantized. We also discuss the general problem of eigenvectors and eigenvalues of a given class of Hamiltonians. We examine obtained exact solutions for the particular case of the electron motion in a rotating neutron star with account for matter and magnetic field effects. We argue that all of these considerations can be usefull for astrophysical applications.
A massive neutrino has nonzero magnetic moment and is involved in the electromagnetic interactions with external fields and photons. The electromagnetic neutrino moving in matter can emit the spin light [Formula: see text] in the process of transition between two quantum states in matter. In quite resembling way an electron can emit spin light in moving background composed of neutrinos, that is “the spin light of an electron in neutrino flux” [Formula: see text]. In this paper we obtain the exact solution for the wave function and energy spectrum for an electron moving in a neutrino flux and consider the [Formula: see text] as the transition process between two electron quantum states in the background. The [Formula: see text] radiation rate, power and emitted photon energy are calculated. Notably, the energy spectrum of the emitted [Formula: see text] photons can span up to gamma-rays. We argue that the considered [Formula: see text] can be of interest for astrophysical applications, for supernovae processes in particular.
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