  Based on the Bohr's correspondence principle it is shown that relativistic
mechanics and quantum mechanics may be considered as generalizations of
classical mechanics. A comparative description of relativistic and classical
mechanics is given using three main principles: the definition of momentum, the
main law of dynamics (Newton's second law) and the law of conservation of
energy. The difference of relativistic mechanics from classical mechanics is
due to the new definition of momentum that is proportional to energy and
velocity. It is shown that new relativistic laws of dynamics make it necessary
to change kinematical relations of classical mechanics such as the law of
velocity composition, coordinate transformation etc. It is demonstrated that
quantum mechanics may be considered as a rational statistical generalization of
classical mechanics. Statistical conformities in quantum mechanics are
fundamental and are not due to the incomplete information about the system.
  From all possible multi-parametric statistical models the root model is most
remarkable. Constructing of a root multi-parametric statistical model leads to
obtaining such frequencies and base functions in Fourier decomposition so that
classical laws of motion are fulfilled in average. Root model leads to a
consistent condition that connects eigenvectors and eigenvalues of a mechanical
system that is described by a matrix equation of Heisenberg. Matrix equation of
Heisenberg leads to an operator equation. The solution of the operator equation
may be considered as the construction of Hamiltonian of the system and a move
to the Schrodinger representation. The considered approach naturally leads to
the notion of momentum operator, fundamental commutation relations, density
matrix and Liouville equation construction etc.
