Localized nonspreading solutions of massless wave equations with class
ical parameters (initial position x0 of the center of the wave, intern
al frequency OMEGA, intial velocity v0) describe single quantum events
, and when averaged over these parameters they reproduce probabilistic
wave functions, e.g. in interference phenomena. They propagate as qua
ntum particles with dispersion relation of a massive particle. We cons
truct here explicitly such solutions for the massless Dirac equation,
Weyl equation, and as a limiting case, the Pauli equation.