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Physical Review A

Comment on ‘‘Density-matrix formulation ofab initiomethods of nonrelativistic quantum mechanics’’

Jerzy Ciosłowski, Mel Levy

Published Dec 1, 1989• 1 citation
Publisher

Abstract

Most of the results of the recent paper by A. Redondo [Phys. Rev. A 39, 4366 (1989)] are both well-known and well documented in literature. Parts of the first-order density matrix history are briefly reviewed.
DOI
10.1103/physreva.40.6727

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A missing paragraph from the original work [A. Redondo, Phys. Rev. A 39, 4366 (1989] that is being commented upon [preceding paper, Cioslowski and Levy, Phys. Rev. A 40, 6727 (1989)] is included. The relationship between this work and a theorem by Lieb [E. Lieb, Phys. Rev. Lett. 46, 457 (1981); 47, 69 (1981)] is also noted.

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A density-matrix formulation of the ab initio methods of nonrelativistic quantum mechanics is presented. The variational equations for the standard calculational techniques of molecular quantum mechanics are derived from a single expression for the total energy of an N-particle system. A generalization of the Hohenberg-Kohn theorem is proved, showing that the ground-state energy of a many-body Hamiltonian is a functional of the single-particle density matrix and hence of the first-order reduced-density function (the diagonal of which is the particle density of the standard theorem). The theorem is used to develop a new method to calculate the total energy and single-particle properties of the many-body problem.
I briefly review the "decohering histories" or "consistent histories" formulation of quantum theory, due to Griffiths, Omnès, and Gell-Mann and Hartle (and the subject of my graduate work with George Sudarshan). I also sift through the many meanings that have been attached to decohering histories, with an emphasis on the most basic one: Decoherence of appropriate histories is needed to establish that quantum mechanics has the correct classical limit. Then I will describe efforts to find physical mechanisms that do this. Since most work has focused on density matrix versions of decoherence, I'll consider the relation between the two formulations, which historically has not been straightforward. Finally, I'll suggest a line of research that would use recent results by Sudarshan to illuminate this aspect of the classical limit of quantum theory.