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

A variational method is constructed that reduces the many-particle problem for the ground state of a quantum-mechanical system to the solution of one equation for the function of a local scale transformation. A theorem is proved that provides a rigorous basis of the widely used density functional method. For a fairly general form of the Hamiltonian of the system, stationarity equations are obtained explicitly together with a condition under which the solution minimizes the energy of the system. The possibility of practical application of the method is discussed.