Density matrices derived from polynomial approximations and other models

An explicit relation between the density matrix and its s-state part is derived for electron closed shells moving in a bare Coulomb potential, thus extending previous work of one of us [N. H. March, Phys. Rev. A 33, 88 (1986)] to off-diagonal elements of the density matrix. Further polynomial models are considered and generalization of previously known relations is sought. For one-dimensional polynomial approximations it is shown that the wave function assumes a definite form irrespective of the weight function so that there is no need for the calculation of the coefficients of the orthogonal polynomials for determining the density matrix. The use of the established relations in functional theories is also discussed.