  We revise the problem of the quantization of relativistic particle,
presenting a modified consistent canonical scheme, which allows one not only to
include arbitrary backgrounds in the consideration but to get in course of the
quantization a consistent relativistic quantum mechanics, which reproduces
literally the behavior of the one-particle sector of the corresponding quantum
field. At the same time this construction presents a possible solution of the
well-known old problem how to construct a consistent quantum mechanics on the
base of a relativistic wave equation.
