Dispersion chain of quantum mechanics equations

Abstract

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.