  Covariant classical particle dynamics is described, and the associated
covariant relativistic particle quantum mechanics is derived. The invariant
symmetric bracket is defined on the space of quantum amplitudes, and its
relation to a generalized Hamiltonian dynamics and to a covariant Schr\"odinger
type equation is shown. Examples for relativistic potential problems are
solved. Mathematically and physically acceptable probability densities for the
Klein-Gordon equation and for the Dirac equation are derived, and a new
continuity equation for each case is given. The quantum distribution for mass
is discussed, and unambiguous representations of four-velocity and
four-acceleration operators are given.
