  The exact quantum-mechanical equations for beams of free particles including
photons and for beams of Dirac and spin-1 particles in a uniform magnetic field
have been derived. These equations present the exact generalizations of the
well-known paraxial equations in optics (exact Helmholtz equation for light
beams) and particle physics and of the previously obtained paraxial equation
for a Dirac particle in a uniform magnetic field. Some basic properties of
exact wave eigenfunctions of particle beams have been determined.
