  Axion-photon conversion at dielectric interfaces, immersed in a
near-homogeneous magnetic field, is the basis for the dielectric haloscope
method to search for axion dark matter. In analogy to transition radiation,
this process is possible because the photon wave function is modified by the
dielectric layers ("Garibian wave function") and is no longer an eigenstate of
momentum. A conventional first-order perturbative calculation of the transition
probability between a quantized axion state and these distorted photon states
provides the microwave production rate. It agrees with previous results based
on solving the classical Maxwell equations for the combined system of axions
and electromagnetic fields. We argue that in general the average photon
production rate is given by our result, independently of the detailed quantum
state of the axion field. Moreover, our result provides a new perspective on
axion-photon conversion in dielectric haloscopes because the rate is based on
an overlap integral between unperturbed axion and photon wave functions, in
analogy to the usual treatment of microwave-cavity haloscopes.
