Slater sum for an inhomogeneous liquid of Fermions generated by a sech2 x potential in one dimension

Abstract

In one dimension, the Slater sum S(x, β), which is the diagonal element of the canonical density matrix, satisfies a known partial differential equation characterised by a one-body potential V(x). Here, for the case of a sech2 x potential in one dimension, it is stressed that S(x, β) is explicitly related to the limit S 0(β) as V(x) → 0 and to V(x) itself. This is the same input information as in the Thomas–Fermi result. The relevance to density functional theory is emphasised.