Density Matrix Method in Atom Theory

In this work, we apply a new variational principle that allows us to find the distribution function of electron in an arbitrary atom. This principle is based on the method of density matrix. Using the density matrix, we found the energy of the electrons in an atom, entropy and thermodynamic potential. The main idea of this article is that all two-electron matrices must be anti-symmetric. This refers to the two-electron Hamiltonian. This applies to Slater two-particle wave function. We found the equation for the distribution function of electrons at the quantum orbits. This equation can be obtained in two cases. In the first case, based on the density matrix of the first order, this equation is obtained only for the distribution function. In the second case two equations are obtained, which include distribution function and correlation function. The distribution function of electrons in the atom is similar to the function of Fermi-Dirac for electrons in a solid. In this work we apply a new approach to calculate the energy levels of electron in an arbitrary atom. This approach is also based on the method of density matrix.