Campus Units

Physics and Astronomy, Mathematics, Chemistry, Ames Laboratory

Document Type

Article

Publication Version

Published Version

Publication Date

1985

Journal or Book Title

The Journal of Chemical Physics

Volume

83

Issue

4

First Page

1637

Last Page

1647

DOI

10.1063/1.449401

Abstract

Local, i.e., multiplicative, operators satisfy well‐known linear factorization relations wherein matrix elements (between states associated with a complete set of wave functions) can be obtained as a linear combination of those out of the ground state (the input data). Analytic derivation of factorization relations for general state input data results in singular integral expressions for the coefficients, which can, however, be regularized using consistency conditions between matrix elements out of a single (nonground) state. Similar results hold for suitable ‘‘symmetry class’’ averaged matrix elements where the symmetry class projection operators are ‘‘complete.’’ In several cases where the wave functions or projection operators incorporate orthogonal polynomial dependence, we show that the ground state factorization relations have a simplified structure allowing an alternative derivation of the general factorization relations via an infinite matrix inversion procedure. This form is shown to have some advantages over previous versions. In addition, this matrix inversion procedure obtains all consistency conditions (which is not always the case from regularization of singular integrals).

Comments

This article is published as Chan, C. K., D. K. Hoffman, and J. W. Evans. "General factorization relations and consistency conditions in the sudden approximation via infinite matrix inversion." The Journal of chemical physics 83, no. 4 (1985): 1637-1647, doi:10.1063/1.449401. Posted with permission.

Copyright Owner

American Institute of Physics

Language

en

File Format

application/pdf

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