Integral representation of the Coulomb Green function derived from the Sturmian expansion

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 70, Issue 4, 2004, Pages

  Shakeshaft, Robin ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DECOMPOSITION; EIGENVALUES AND EIGENFUNCTIONS; GREEN'S FUNCTION; HYDROGEN; MATRIX ALGEBRA; PHOTONS;

COULOMB GREEN FUNCTION; EIGENVALUE SPECTRUM; INTEGRAL REPRESENTATION; STURMIAN EXPANSION;

QUANTUM THEORY;

EID: 19744381034     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.042704     Document Type: Article

References (19)

1. M. Rotenberg, Adv. At. Mol. Phys. 6, 233 (1970).
2. +) are also very useful. See S. Yu. Ovchinnikov, G. N. Orgurtsov, and J. H. Macek, Phys. Rep. 389, 119 (2004).
3. S. Klarsfeld and A. Maquet, Phys. Lett. 73A, 100 (1979).
4. S. Klarsfeld and A. Maquet, J. Phys. B 12, L553 (1979).
5. Z. Papp, J. Phys. A 20, 153 (1987).
6. Z. Papp, C.-Y. Hu, Z. T. Hlousek, B. Konya, and S. L. Yakolev, Phys. Rev. A 63, 062721 (2001).
7. Z. Papp, J. Darai, C.-Y. Hu, Z. T. Hlousek, B. Konya, and S. L. Yakolev, Phys. Rev. A 65, 032725 (2002).
8. L. C. Hostler, J. Math. Phys. 11, 2966 (1970).
9. M. Abramowitz and I. E. Stegun, Handbook of Mathematical Functions (U.S. GPO, Washington, DC, 1964).
10. See, e.g., formula 15.3.12 of Ref. [9] in the limit where the second argument of the hypergeometric function becomes a negative integer.
11. F. L. Yost, J. A. Wheeler, and G. Breit, Phys. Rev. 49, 174 (1936). See also formula 13.3.8 of Ref. [9].
12. 0+i0+ε), and apply the Cauchy theorem.
13. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, Baltimore, 1996).
14. K. Frankowski and C. L. Pekeris, Phys. Rev. 146, 46 (1966).
15. R. Shakeshaft, Phys. Rev. A 60, 1280 (1999); 60, 4198 (1999).
16. R. Shakeshaft, Phys. Rev. A 60, 1280 (1999); 60, 4198 (1999).
17. A. Kheifets and I. Bray, Phys. Rev. A 58, 4501 (1998).
18. K. W. Meyer, C. H. Greene, and B. D. Esry, Phys. Rev. Lett. 78, 3662 (1997).
19. G. Edah, E. Foumouo, and B. Piraux (private communication).