  Based on the dispersion chain of the Vlasov equations, the paper considers
the construction of a new chain of equations of quantum mechanics of high
kinematical values. The proposed approach can be applied to consideration of
classical and quantum systems with radiation. A number of theorems are proved
on the form of extensions of the Hamilton operators, Lagrange functions,
Hamilton-Jacobi equations, and Maxwell equations to the case of a generalized
phase space. In some special cases of lower dimensions, the dispersion chain of
quantum mechanics is reduced to quantum mechanics in phase space (the Wigner
function) and the de Broglie-Bohm {\guillemotleft}pilot wave{\guillemotright}
theory. An example of solving the Schr\"odinger equation of the second rank
(for the phase space) is analyzed, which, in contrast to the Wigner function,
gives a positive distribution density function.
