Unified treatment of complete orthonormal sets for wave functions, and Slater orbitals of particles with arbitrary spin in coordinate, momentum and four-dimensional spaces


Guseinov I. I.

PHYSICS LETTERS A, cilt.372, ss.44-48, 2007 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 372 Konu: 1
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1016/j.physleta.2007.07.005
  • Dergi Adı: PHYSICS LETTERS A
  • Sayfa Sayıları: ss.44-48

Özet

The new analytical relations of complete orthonormal sets for the tensor wave functions and the tensor Slater orbitals of particles with arbitrary spin in coordinate, momentum and four-dimensional spaces are derived using the properties of tensor spherical harmonics and complete orthonormal scalar basis sets of psi(alpha)-exponential type orbitals, phi(alpha)-momentum space orbitals and z(alpha)-hyperspherical harmonics introduced by the author for particles with spin s = 0, where the alpha = 1, 0, -1, -2,.... All of the tensor wave functions obtained are complete without the inclusion of the continuum and, therefore, their group of transformations is the four-dimensional rotation group O(4). The analytical formulas in coordinate space are also derived for the overlap integrals over tensor Slater orbitals with the same screening constant. We notice that the new idea presented in this work is the combination of tensor spherical harmonics of rank s with complete orthonormal scalar sets for radial parts of psi(alpha)-, phi(alpha)- and z(alpha)-orbitals, where s = 1/2, 1, 3/2, 2,.... (c) 2007 Elsevier B.V. All rights reserved.