Abstract The derivation of the connected moments expansion (CMX) is examined as well as the singularities that arise in the series expansion for the ground‐state energy. Explicit analytic results are presented that show a canceling of these singularities. Also, an alternate moments expansion (AMX) is derived that closely models the CMX but displays a varied computational range. © 1994 John Wiley & Sons, Inc.

International Journal of Quantum ChemistryApr 5, 199438 citations

Lecture notes in physics

Derivative Expansion

Peter Kopietz, Lorenz Bartosch, Florian Schütz

Published Dec 25, 2009• 1 citation

Publisher

DOI: 10.1007/978-3-642-05094-7_9

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The binary collision expansion for the density matrix of a system of

N

particles with pair interaction was derived by Huang, Lee, and Yang by expansion in the interaction and subsequent summation over terms represented by certain classes of diagrams. A simpler derivation has been obtained by the use of the $\frac{N(N\ensuremath{-}1)}{2}$ integral equations which relate the density matrix of the system to the density matrices of systems in which only one pair of particles interacts. Successive substitution of the integral equations into each other yields an expansion which by a trivial additional step becomes the binary collision expansion. Our derivation shows also that the binary collision expansion is the Laplace inverse of the coordinate representation of the expansion in terms of scattering operators.