Perturbation Expansion Of The Single‐particle Density Matrix

Abstract

An expansion theorem for the matrix element of an operator, previously used by Schafroth, is shown to be equivalent to the resolvent method and is used to obtain a perturbation series expansion of the density matrix which is analogous to the Born series of time‐independent scattering theory. Green's perturbation formula for the density matrix of N distinguishable particles follows quite easily. The method is applied in the self‐consistent field approximation to the potential of an impurity in a solid of arbitrary degeneracy, and for both free and Bloch electrons. The perturbed electron density is given to all orders in the impurity potential, the linear term being what the static dielectric theory gives. For metals at finite temperatures the screening function is damped by a factor which is similar to the damping factor of the Friedel oscillations. The screening condition is discussed briefly in this formulation. The passage from the perturbation expansion to the Thomas‐Fermi approximation is pointed out. Copyright © 1979 John Wiley & Sons, Inc.

Department(s)

Physics

International Standard Serial Number (ISSN)

1097-461X; 0020-7608

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Wiley, All rights reserved.

Publication Date

01 Jan 1979

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