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

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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 Ψα-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.

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  1. Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Çanakkale, Turkey

    I. I. Guseinov

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  1. I. I. Guseinov
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Correspondence to I. I. Guseinov.

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Guseinov, I.I. Unified treatment of complete orthonormal sets of functions in coordinate, momentum and four-dimensional spaces and their expansion and one-range addition theorems. J Math Chem 42, 991–1001 (2007). https://doi.org/10.1007/s10910-006-9154-1

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  • DOI: https://doi.org/10.1007/s10910-006-9154-1

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