Local scale transformation method for the ground state of many-particle systems

A variational method is proposed which reduces the problem of finding the ground state of many-particle quantum-mechanical system to the solution of a single equation for the function of local scale transformation. The theorem for the local-density energy functional is proved which provides a rigorous ground for the widely used density functional method. For a sufficiently general form of the hamiltonian of the system the authors have explicitly obtained the stationarity equation and the condition under which its solution minimizes the energy of the system. The possibility for the practical applications of the method is discussed