BIPOLAR EXPANSION OF SCREENED COULOMB POTENTIALS, HELMHOLTZ' SOLID HARMONICS, AND THEIR ADDITION THEOREMS.

Abstract

Helmholtz' solid harmonics (spherical Bessel functions X spherical surface harmonics) are generated from fundamental spherical waves through a ladder procedure using raising and lowering operators. The addition theorem for them and the bipolar expansion formula of a screened Coulomb potential are derived. A method for evaluating two-center integrals with a general potential is given which is new and useful in practical calculations. Lastly, a key function, which appears in all the essential results, is studied in detail. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1965
Accession Number
AD0631292

Entities

People

  • Reikichi Nozawa

Organizations

  • Uppsala University

Tags

DTIC Thesaurus Topics

  • Bessel Functions
  • Functions (Mathematics)
  • Harmonics
  • Integrals
  • Mathematics
  • Spherical Waves
  • Waves

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.