Метод координатной функции Фока, интегральные соотношения между спиновыми и зарядовыми плотностями, их свойства

Abstract

The practical consequence of the Fock coordinate wave function method in form of the general integral relation between Fock functions reduced density matrices (RDM) with different number of particles has been obtained in the preceding article. This result was applied here for determining the integral relationships between spin and charge densities. These relations are obtained by solving systems of equations that have been proposed and ones have been written at Fock functions RDM basis. And also the special cases of the general integral relation of the previous article have been considered. The last cases were used to obtain the expansions on the basis of the RDM of Fock functions for the partial integrals of the charge densities having the transpositions of their coordinates. This is not as straightforward as it may seem, since the multiple character of integral relations are existing. But applied method allows obtaining the different forms of such relations in the strict sense. Moreover the identity of ambiguity forms of writing has been proved. In the conducted transformations used only densities that depend on spatial coordinates of electrons. Therefore this approach added to the methods of spin free quantum mechanics new attack on the problem of spin distributions. The results of preceding articles have been touched. The full integral value for the two-, three- and four-particle charge densities having transpositions, which act on them on one side, were calculated, and its physical sense have been discussed also. The all received results do not depend on the used approached model for calculations of quantum mechanical system state, because ones are exact. Hence all such results can be applied to check of the fidelity of construction both the appropriate charge densities and the approached model wave function, which used.