  In this work, I study the mixing of photons with pseudoscalar particles and
vice-versa in the presence of an external magnetic field and a pseudoscalar
field. I solve exactly for the first time in the literature the equations of
motion of the electromagnetic field coupled with a pseudoscalar field in the
presence of a constant magnetic field with arbitrary direction with respect to
the direction of propagation of the fields in vacuum. In addition, I also solve
exactly the equations of motion in a magnetized plasma/gas for perpendicular
propagation with respect to the external magnetic field. By finding exact
solutions to the equations of motion, I find exact expressions for the
transition efficiencies of photons into pseudoscalar particles in different
situations. The expressions of the transition efficiencies generalize and
correct those previously found in the literature by using approximate WKB
methods on solving the equations of motion. In the case when the direction of
propagation of fields with respect to the external magnetic field is not
perpendicular, a longitudinal state of the electromagnetic field is generated
even in a magnetized vacuum. The appearance of the longitudinal electric field
state could be used for laboratory searches of pseudoscalar particles such as
the axion and/or axion-like particles.
