#### Sponsor

This work was supported by the U. S. Office of Naval Research.

#### Published In

Physical Review A

#### Document Type

Article

#### Publication Date

3-1987

#### Subjects

Legendre's functions, Fourier transformations, Orthogonalization methods, Atomic orbitals

#### Abstract

Integrating the radial part of the Fourier transform of the product of *N* hydrogenic orbitals results in an associated Legendre function that can be reduced to a finite series of elementary functions. This transform is found to depend on a polynomial in the wave vector *k* divided by a binomial in *k*^{2}* *raised to a power that is the sum of principle quantum numbers. This form facilitates the analytical reduction of integrals arising from orthogonalization corrections in atomic processes. Transforms for the product of orbital pairs (*1s*,*1s*) through (*1s*,*3d*) are given explicitly.

#### DOI

10.1103/PhysRevA.35.2729

#### Persistent Identifier

http://archives.pdx.edu/ds/psu/11001

#### Citation Details

Straton, Jack C. "Fourier transform of the product of N one-center hydrogenic orbitals." Physical Review A 35.6 (1987): 2729. DOI: http://dx.doi.org/10.1103/PhysRevA.35.2729

## Description

This is the publisher's final PDF. Article appears in Physical Review A (http://pra.aps.org/) and is copyrighted by APS Journals (http://publish.aps.org/).

At the time of publication Jack Straton was employed at the University of Oregon.