Dirac Delta Functions in the Laplace-Type Expansion of rnYlm(θ, φ)
- 15 September 1969
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 51 (6) , 2359-2362
- https://doi.org/10.1063/1.1672352
Abstract
The theory of generalized functions and Fourier transforms is used to derive the Laplace‐type expansion for r 12 n Y l m (θ 12 , φ 12 ) . This approach leads naturally to a general formula for the Dirac delta‐function terms which occur when n≤−3 and n − l is odd.Keywords
This publication has 6 references indexed in Scilit:
- Expansion about an Arbitrary Point of Three-Dimensional Functions Involving Spherical Harmonics by the Fourier-Transform Convolution TheoremThe Journal of Chemical Physics, 1967
- Expansion theorems for solid spherical harmonicsMolecular Physics, 1965
- Irreducible Tensor Expansion of Solid Spherical Harmonic-Type Operators in Quantum MechanicsJournal of Mathematical Physics, 1964
- Generalization of Laplace's Expansion to Arbitrary Powers and Functions of the Distance between Two PointsJournal of Mathematical Physics, 1964
- Evaluation of Molecular Integrals by Solid Spherical Harmonic ExpansionsThe Journal of Chemical Physics, 1962
- The Electrostatic Interaction of Two Arbitrary Charge DistributionsJournal of Mathematics and Physics, 1958