Related Experiment Video
Updated: Aug 17, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
Direct determination of multipole moments of Cartesian Gaussian functions in spherical polar coordinates
1Department of Chemistry, College of Natural Sciences, Kyungpook National University, Taegu 702-701, South Korea. cchoi@knu.ac.kr
Abstract:
A new way of generating the multipole moments of Cartesian Gaussian functions in spherical polar coordinates has been established, bypassing the intermediary of Cartesian moment tensors. A new set of recurrence relations have also been derived for the resulting analytic integral values. The new method furnishes a conceptually simple and numerically efficient evaluation procedure for the multipole moments. The advantages over existing methods are documented. The results are relevant for the linear scaling quantum theories based on the fast multipole method.
Related Concept Videos
Polar and Cylindrical Coordinates
Gauss's Law: Spherical Symmetry
Spherical Coordinates
Polar Coordinates
Graphs of Polar Equations
Triple Integrals in Spherical Coordinates

