Exact L2 series solution of the Dirac-Coulomb problem for all energies

Annals of Physics

Volumn 312, Issue 1, 2004, Pages 144-160

  Alhaidari, A D ^a  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Coulomb potential; Dirac equation; Pollaczek polynomials; Recursion relations; Relativistic spectrum; Scattering; Tridiagonal representations

Indexed keywords

EID: 3142699169     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aop.2004.01.011     Document Type: Article

References (62)

1. See, for example Natanzon G.A. Teor. Mat. Fiz. 38 1979 219
2. Gendenshtein L.E. Zh. Eksp. Teor. Fiz. Pis'ma Red 38 1983 299
3. Cooper F. Ginocchi J.N. Khare A. Phys. Rev. D 36 1987 2458
4. Dutt R. Khare A. Sukhatme U.P. Am. J. Phys. 56 1988 163
5. Am. J. Phys. 59 1991 723
6. Lévai G. J. Phys. A 22 1989 689
7. J. Phys. A 27 1994 3809
8. See for example Witten E. Nucl. Phys. B 185 1981 513
9. Cooper F. Freedman B. Ann. Phys. (NY) 146 1983 262
10. Sukumar C.V. J. Phys. A 18 1985 2917
11. Arai A. J. Math. Phys. 30 1989 1164
12. Cooper F. Khare A. Sukhatme U. Phys. Rep. 251 1995 267
13. See, for example Wybourne B.G. Classical Groups for Physicists 1974 Wiley-Interscience New York
14. Miller W.Jr Lie Theory and Special Functions 1968 Academic New York
15. Alhassid Y. Gürsey F. Iachello F. Phys. Rev. Lett. 50 1983 873
16. Ann. Phys. (NY) 148 1983 346
17. Ann. Phys. (NY) 167 1986 181
18. Alhassid Y. Iachello F. Levine R.D. Phys. Rev. Lett. 54 1985 1746
19. Alhassid Y. Iachello F. Wu J. Phys. Rev. Lett. 56 1986 271
20. Wu J. Alhassid Y. J. Math. Phys. 31 1990 557
21. Englefield M.J. Quesne C. J. Phys. A 24 1991 3557
22. Manning M.F. Phys. Rev. 48 1935 161
23. Bhattacharjie A. Sudarshan E.C.G. Nuovo Cimento 25 1962 864
24. Pak N.K. Sökmen I. Phys. Lett. 103A 1984 298
25. Goldstein H.G. Classical Mechanics 1986 Addison-Wesley Reading-MA
26. Montemayor R. Phys. Rev. A 36 1987 1562
27. Junker G. J. Phys. A 23 1990 L881
28. De R. Dutt R. Sukhatem U. J. Phys. A 25 1992 L843
29. de Souza-Dutra A. Phys. Rev. A 47 1993 R2435
30. Nag N. Roychoudhury R. Varshni Y.P. Phys. Rev. A 49 1994 5098
31. Dutt R. Khare A. Varshni Y.P. J. Phys. A 28 1995 L107
32. Grosche C. J. Phys. A 28 1995 5889
33. J. Phys. A 29 1996 365
34. Lévai G. Roy P. Phys. Lett. A 270 1998 155
35. Junker G. Roy P. Ann. Phys. (NY) 264 1999 117
36. Roychoudhury R. Roy P. Zonjil M. Lévai G. J. Math. Phys. 42 2001 1996
37. Turbiner A.V. Commun. Math. Phys. 118 1988 467
38. Shifman M.A. Int. J. Mod. Phys. A 4 1989 2897
39. Adhikari R. Dutt R. Varshni Y. Phys. Lett. A 141 1989 1
40. J. Math. Phys. 32 1991 447
41. Roychoudhury R. Varshni Y.P. Sengupta M. Phys. Rev. A 42 1990 184
42. Salem L.D. Montemayor R. Phys. Rev. A 43 1991 1169
43. Lucht M.W. Jarvis P.D. Phys. Rev. A 47 1993 817
44. Ushveridze A.G. Quasi-exactly Solvable Models in Quantum Mechanics 1994 IOP Bristol
45. Alhaidari A.D. Phys. Rev. Lett. 87 2001 210405
46. Phys. Rev. Lett. 88 2002 189901
47. J. Phys. A 34 2001 9827
48. J. Phys. A 35 2002 6207
49. Jian-You G. Xiang Zheng F. Fu-Xin X. Phys. Rev. A 66 2002 062105
50. Guo J.-Y. Meng J. Xu F.-X. Chin. Phys. Lett. 20 2003 602
51. Alhaidari A.D. Int. J. Mod. Phys. A 18 2003 4955
52. Yamani H.A. Reinhardt W.P. Phys. Rev. A 11 1975 1144
53. R. Koekoek, R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Report No. 98-17. Delft University of Technology, Delft, 1998, pp. 37-38
54. Bjorken J.D. Drell S.D. Relativistic Quantum Mechanics 1965 McGraw Hill New York
55. Heller E.J. Yamani H.A. Phys. Rev. A 9 1974 1201
56. Phys. Rev. A 9 1974 1209
57. Yamani H.A. Fishman L. J. Math. Phys. 16 1975 410
58. Broad J.T. Reinhardt W.P. Phys. Rev. A 14 1976 2159
59. Examples of textbooks and monographs on special functions and orthogonal polynomials are: Magnus W. Oberhettinger F. Soni R.P. Formulas and Theorems for the Special Functions of Mathematical Physics 1966 Springer-Verlag New York
60. Chihara T.S. An Introduction to Orthogonal Polynomials 1978 Gordon and Breach New York
61. Szegö G. Orthogonal polynomials fourth ed. 1997 American Mathematical Society Providence, RI
62. R. Askey, M. Ismail, Recurrence relations, continued fractions and orthogonal polynomials, Memoirs of the Am. Math. Soc., vol. 49, Nr. 300 American Mathematical Society, Providence, RI, 1984