  The explicit expression for the inclusive probability to record a photon
created in transition radiation from a one Dirac particle wave packet
traversing an ideally conducting plate is derived in the leading order of
perturbation theory. The anomalous magnetic moment of the Dirac particle is
taken into account. It is shown that the quantum corrections to transition
radiation from an electrically charged particle give rise to production of
photons with polarization vector orthogonal to the reaction plane ($E$-plane).
These corrections result from both the quantum recoil and the finite size of a
wave packet. As for transition radiation produced by a neutron falling normally
onto the conducting plate, the probability to detect a photon with polarization
vector lying in the reaction plane does not depend on the observation angle and
the energy of the incident particle. The peculiarities of transition radiation
stemming from different shapes of the particle wave packet are investigated. In
particular, the transition radiation produced by the wave packet of one twisted
Dirac particle is described. The comparison with classical approach to
transition radiation is given and the quantum formula for the inclusive
probability to detect a photon radiated by the $N$-particle wave packet is
derived.
