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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† |
| Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey |
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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.
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Received: 21 September 2011
Revised: 17 October 2011
Accepted manuscript online:
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PACS:
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31.10.+z
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(Theory of electronic structure, electronic transitions, and chemical binding)
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31.15.-p
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(Calculations and mathematical techniques in atomic and molecular physics)
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31.15.Ar
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Corresponding Authors:
I. I. Guseinov
E-mail: isguseinov@yahoo.com
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Cite this article:
I. I. Guseinov 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 2012 Chin. Phys. B 21 063101
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