Unified treatment of complete orthonormal sets of functions in coordinate, momentum and four-dimensional spaces and their expansion and one-range addition theorems

Guseinov I. I.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.42, sa.4, ss.991-1001, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 4
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1007/s10910-006-9154-1
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.991-1001
  • Çanakkale Onsekiz Mart Üniversitesi Adresli: Hayır

Özet

The simpler formulas are derived for the complete orthonormal sets of exponential- type orbitals, momentum space orbitals and hyperspherical harmonics and their expansion and one-range addition theorems. The continuum states are not properly included in these functions. The analytical formulas are also obtained for the overlap integrals over Psi(alpha)-ETOs, their extensions to momentum and four-dimensional spaces and STOs with the same screening constants using addition and expansion theorems derived in this paper. The complete orthonormal sets of functions and their expansion and one-range addition theorems obtained can be useful in the study of different quantum mechanical problems when the coordinate, momentum or four-dimensional spaces employed.