中国物理B ›› 2012, Vol. 21 ›› Issue (6): 63101-063101.doi: 10.1088/1674-1056/21/6/063101

• ATOMIC AND MOLECULAR PHYSICS • 上一篇    下一篇

One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces

I. I. Guseinov   

  1. Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey
  • 收稿日期:2011-09-21 修回日期:2011-10-17 出版日期:2012-05-01 发布日期:2012-05-01

One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces

I. I. Guseinov   

  1. Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey
  • Received:2011-09-21 Revised:2011-10-17 Online:2012-05-01 Published:2012-05-01
  • Contact: I. I. Guseinov E-mail:isguseinov@yahoo.com

摘要: The formulae are established in position, momentum, and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine (GCTCP and GETCP HC). These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of Ψα -exponential type orbitals (Ψα -ETO), φα -momentum space orbitals (φα -MSO), and zα -hyperspherical harmonics (zα-HSH) introduced. The one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position, momentum, and four-dimensional spaces are employed.

关键词: correlated interaction potentials, one-range additional theorems, complete orthonormal sets of orbitals, overlap integrals

Abstract: The formulae are established in position, momentum, and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine (GCTCP and GETCP HC). These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of Ψα -exponential type orbitals (Ψα -ETO), φα -momentum space orbitals (φα -MSO), and zα -hyperspherical harmonics (zα-HSH) introduced. The one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position, momentum, and four-dimensional spaces are employed.

Key words: correlated interaction potentials, one-range additional theorems, complete orthonormal sets of orbitals, overlap integrals

中图分类号:  (Theory of electronic structure, electronic transitions, and chemical binding)

  • 31.10.+z
31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)