  We develop a new concept of quantum mechanics which is based on a generalized
space-time and on an action vector space similar to it. Both spaces are
provided by algebraic properties. This allows to calculate the Dirac matrixes
and to derive quantum mechanics equations from structure equations of the
specified algebras. A new interpretation of the wave function is given as
differential of the action vector. A generalization of the Dirac equation for
8-component wave function is derived. It is interpreted as the equation for two
leptons of the same generation. A procedure of the approximate description of
free leptons is formulated. The generalized equation of quantum mechanics is
reduced to the Dirac, Pauli and Schr\"odinger equations by the sequential use
of this procedure. We explain the existence of three lepton generations.
