Solution of the Dirac equation for potential interaction

International Journal of Modern Physics A

Volumn 18, Issue 27, 2003, Pages 4955-4973

  Alhaidari, A D ^a  

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

Author keywords

Dirac equation; Energy spectrum; Exact solutions; Point canonical transformations; Relativistic potentials

Indexed keywords

CALCULATION; CANONICAL ANALYSIS; ELECTROMAGNETIC FIELD; ENERGY; MATHEMATICAL ANALYSIS; MATHEMATICS; OSCILLATOR; PARAMETER; PHYSICS; REPRODUCIBILITY; REVIEW; SPECTRUM;

EID: 0344012665     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X03015751     Document Type: Review

References (68)

1. See, for example, G. A. Natanzon, Teor. Mat. Fiz. 38, 219 (1979); [Theor. Math. Phys. 38, 146 (1979)]; L. E. Gendenshtein, Zh. Eksp. Teor. Fiz. Pis'ma Red. 38, 299 (1983); [JETP Lett. 38, 356 (1983)]; F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); R. Dutt, A. Khare and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988); ibid. 59, 723 (1991); G. Lévai, J. Phys. A22, 689 (1989); ibid. 27, 3809 (1994).
2. See, for example, G. A. Natanzon, Teor. Mat. Fiz. 38, 219 (1979); [Theor. Math. Phys. 38, 146 (1979)]; L. E. Gendenshtein, Zh. Eksp. Teor. Fiz. Pis'ma Red. 38, 299 (1983); [JETP Lett. 38, 356 (1983)]; F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); R. Dutt, A. Khare and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988); ibid. 59, 723 (1991); G. Lévai, J. Phys. A22, 689 (1989); ibid. 27, 3809 (1994).
3. See, for example, G. A. Natanzon, Teor. Mat. Fiz. 38, 219 (1979); [Theor. Math. Phys. 38, 146 (1979)]; L. E. Gendenshtein, Zh. Eksp. Teor. Fiz. Pis'ma Red. 38, 299 (1983); [JETP Lett. 38, 356 (1983)]; F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); R. Dutt, A. Khare and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988); ibid. 59, 723 (1991); G. Lévai, J. Phys. A22, 689 (1989); ibid. 27, 3809 (1994).
4. See, for example, G. A. Natanzon, Teor. Mat. Fiz. 38, 219 (1979); [Theor. Math. Phys. 38, 146 (1979)]; L. E. Gendenshtein, Zh. Eksp. Teor. Fiz. Pis'ma Red. 38, 299 (1983); [JETP Lett. 38, 356 (1983)]; F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); R. Dutt, A. Khare and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988); ibid. 59, 723 (1991); G. Lévai, J. Phys. A22, 689 (1989); ibid. 27, 3809 (1994).
5. See, for example, G. A. Natanzon, Teor. Mat. Fiz. 38, 219 (1979); [Theor. Math. Phys. 38, 146 (1979)]; L. E. Gendenshtein, Zh. Eksp. Teor. Fiz. Pis'ma Red. 38, 299 (1983); [JETP Lett. 38, 356 (1983)]; F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); R. Dutt, A. Khare and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988); ibid. 59, 723 (1991); G. Lévai, J. Phys. A22, 689 (1989); ibid. 27, 3809 (1994).
6. See, for example, G. A. Natanzon, Teor. Mat. Fiz. 38, 219 (1979); [Theor. Math. Phys. 38, 146 (1979)]; L. E. Gendenshtein, Zh. Eksp. Teor. Fiz. Pis'ma Red. 38, 299 (1983); [JETP Lett. 38, 356 (1983)]; F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); R. Dutt, A. Khare and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988); ibid. 59, 723 (1991); G. Lévai, J. Phys. A22, 689 (1989); ibid. 27, 3809 (1994).
7. See, for example, G. A. Natanzon, Teor. Mat. Fiz. 38, 219 (1979); [Theor. Math. Phys. 38, 146 (1979)]; L. E. Gendenshtein, Zh. Eksp. Teor. Fiz. Pis'ma Red. 38, 299 (1983); [JETP Lett. 38, 356 (1983)]; F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); R. Dutt, A. Khare and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988); ibid. 59, 723 (1991); G. Lévai, J. Phys. A22, 689 (1989); ibid. 27, 3809 (1994).
8. See, for example, G. A. Natanzon, Teor. Mat. Fiz. 38, 219 (1979); [Theor. Math. Phys. 38, 146 (1979)]; L. E. Gendenshtein, Zh. Eksp. Teor. Fiz. Pis'ma Red. 38, 299 (1983); [JETP Lett. 38, 356 (1983)]; F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); R. Dutt, A. Khare and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988); ibid. 59, 723 (1991); G. Lévai, J. Phys. A22, 689 (1989); ibid. 27, 3809 (1994).
9. See, for example, G. A. Natanzon, Teor. Mat. Fiz. 38, 219 (1979); [Theor. Math. Phys. 38, 146 (1979)]; L. E. Gendenshtein, Zh. Eksp. Teor. Fiz. Pis'ma Red. 38, 299 (1983); [JETP Lett. 38, 356 (1983)]; F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); R. Dutt, A. Khare and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988); ibid. 59, 723 (1991); G. Lévai, J. Phys. A22, 689 (1989); ibid. 27, 3809 (1994).
10. M. F. Manning, Phys. Rev. 48, 161 (1935); A. Bhattacharjie and E. C. G. Sudarshan, Nuovo Cimento 25, 864 (1962); N. K. Pak and I. Sökmen, Phys. Lett. A103, 298 (1984); H. G. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Massachussetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
11. M. F. Manning, Phys. Rev. 48, 161 (1935); A. Bhattacharjie and E. C. G. Sudarshan, Nuovo Cimento 25, 864 (1962); N. K. Pak and I. Sökmen, Phys. Lett. A103, 298 (1984); H. G. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Massachussetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
12. M. F. Manning, Phys. Rev. 48, 161 (1935); A. Bhattacharjie and E. C. G. Sudarshan, Nuovo Cimento 25, 864 (1962); N. K. Pak and I. Sökmen, Phys. Lett. A103, 298 (1984); H. G. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Massachussetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
13. M. F. Manning, Phys. Rev. 48, 161 (1935); A. Bhattacharjie and E. C. G. Sudarshan, Nuovo Cimento 25, 864 (1962); N. K. Pak and I. Sökmen, Phys. Lett. A103, 298 (1984); H. G. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Massachussetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
14. M. F. Manning, Phys. Rev. 48, 161 (1935); A. Bhattacharjie and E. C. G. Sudarshan, Nuovo Cimento 25, 864 (1962); N. K. Pak and I. Sökmen, Phys. Lett. A103, 298 (1984); H. G. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Massachussetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
15. M. F. Manning, Phys. Rev. 48, 161 (1935); A. Bhattacharjie and E. C. G. Sudarshan, Nuovo Cimento 25, 864 (1962); N. K. Pak and I. Sökmen, Phys. Lett. A103, 298 (1984); H. G. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Massachussetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
16. See, for example, E. Witten, Nucl. Phys. B185, 513 (1981); F. Cooper and B. Freedman, Ann. Phys. (N. Y.) 146, 262 (1983); C. V. Sukumar, J. Phys. A18, 2917 (1985); A. Arai, J. Math. Phys. 30, 1164 (1989); F. Cooper, A. Khare and U. Sukhatme, Phys. Rep. 251, 267 (1995).
17. See, for example, E. Witten, Nucl. Phys. B185, 513 (1981); F. Cooper and B. Freedman, Ann. Phys. (N. Y.) 146, 262 (1983); C. V. Sukumar, J. Phys. A18, 2917 (1985); A. Arai, J. Math. Phys. 30, 1164 (1989); F. Cooper, A. Khare and U. Sukhatme, Phys. Rep. 251, 267 (1995).
18. See, for example, E. Witten, Nucl. Phys. B185, 513 (1981); F. Cooper and B. Freedman, Ann. Phys. (N. Y.) 146, 262 (1983); C. V. Sukumar, J. Phys. A18, 2917 (1985); A. Arai, J. Math. Phys. 30, 1164 (1989); F. Cooper, A. Khare and U. Sukhatme, Phys. Rep. 251, 267 (1995).
19. See, for example, E. Witten, Nucl. Phys. B185, 513 (1981); F. Cooper and B. Freedman, Ann. Phys. (N. Y.) 146, 262 (1983); C. V. Sukumar, J. Phys. A18, 2917 (1985); A. Arai, J. Math. Phys. 30, 1164 (1989); F. Cooper, A. Khare and U. Sukhatme, Phys. Rep. 251, 267 (1995).
20. See, for example, E. Witten, Nucl. Phys. B185, 513 (1981); F. Cooper and B. Freedman, Ann. Phys. (N. Y.) 146, 262 (1983); C. V. Sukumar, J. Phys. A18, 2917 (1985); A. Arai, J. Math. Phys. 30, 1164 (1989); F. Cooper, A. Khare and U. Sukhatme, Phys. Rep. 251, 267 (1995).
21. See, for example, B. G. Wybourne, Classical Groups for Physicists (Wiley-Interscience, New York, 1974), and references therein; W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Gürsey and F. Iachello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N.Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iachello and R. Levine, Phys. Rev. Lett. 54, 1746 (1985); Y. Alhassid, F. Iachello and J. Wu, Phys. Rev. Lett. 56, 271 (1986); J. Wu and Y. Alhassid, J. Math. Phys. 31, 557 (1990); M. J. Englefield and C. Quesne, J. Phys. A24, 3557 (1991).
22. See, for example, B. G. Wybourne, Classical Groups for Physicists (Wiley-Interscience, New York, 1974), and references therein; W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Gürsey and F. Iachello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N.Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iachello and R. Levine, Phys. Rev. Lett. 54, 1746 (1985); Y. Alhassid, F. Iachello and J. Wu, Phys. Rev. Lett. 56, 271 (1986); J. Wu and Y. Alhassid, J. Math. Phys. 31, 557 (1990); M. J. Englefield and C. Quesne, J. Phys. A24, 3557 (1991).
23. See, for example, B. G. Wybourne, Classical Groups for Physicists (Wiley-Interscience, New York, 1974), and references therein; W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Gürsey and F. Iachello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N.Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iachello and R. Levine, Phys. Rev. Lett. 54, 1746 (1985); Y. Alhassid, F. Iachello and J. Wu, Phys. Rev. Lett. 56, 271 (1986); J. Wu and Y. Alhassid, J. Math. Phys. 31, 557 (1990); M. J. Englefield and C. Quesne, J. Phys. A24, 3557 (1991).
24. See, for example, B. G. Wybourne, Classical Groups for Physicists (Wiley-Interscience, New York, 1974), and references therein; W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Gürsey and F. Iachello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N.Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iachello and R. Levine, Phys. Rev. Lett. 54, 1746 (1985); Y. Alhassid, F. Iachello and J. Wu, Phys. Rev. Lett. 56, 271 (1986); J. Wu and Y. Alhassid, J. Math. Phys. 31, 557 (1990); M. J. Englefield and C. Quesne, J. Phys. A24, 3557 (1991).
25. See, for example, B. G. Wybourne, Classical Groups for Physicists (Wiley-Interscience, New York, 1974), and references therein; W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Gürsey and F. Iachello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N.Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iachello and R. Levine, Phys. Rev. Lett. 54, 1746 (1985); Y. Alhassid, F. Iachello and J. Wu, Phys. Rev. Lett. 56, 271 (1986); J. Wu and Y. Alhassid, J. Math. Phys. 31, 557 (1990); M. J. Englefield and C. Quesne, J. Phys. A24, 3557 (1991).
26. See, for example, B. G. Wybourne, Classical Groups for Physicists (Wiley-Interscience, New York, 1974), and references therein; W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Gürsey and F. Iachello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N.Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iachello and R. Levine, Phys. Rev. Lett. 54, 1746 (1985); Y. Alhassid, F. Iachello and J. Wu, Phys. Rev. Lett. 56, 271 (1986); J. Wu and Y. Alhassid, J. Math. Phys. 31, 557 (1990); M. J. Englefield and C. Quesne, J. Phys. A24, 3557 (1991).
27. See, for example, B. G. Wybourne, Classical Groups for Physicists (Wiley-Interscience, New York, 1974), and references therein; W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Gürsey and F. Iachello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N.Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iachello and R. Levine, Phys. Rev. Lett. 54, 1746 (1985); Y. Alhassid, F. Iachello and J. Wu, Phys. Rev. Lett. 56, 271 (1986); J. Wu and Y. Alhassid, J. Math. Phys. 31, 557 (1990); M. J. Englefield and C. Quesne, J. Phys. A24, 3557 (1991).
28. See, for example, B. G. Wybourne, Classical Groups for Physicists (Wiley-Interscience, New York, 1974), and references therein; W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Gürsey and F. Iachello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N.Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iachello and R. Levine, Phys. Rev. Lett. 54, 1746 (1985); Y. Alhassid, F. Iachello and J. Wu, Phys. Rev. Lett. 56, 271 (1986); J. Wu and Y. Alhassid, J. Math. Phys. 31, 557 (1990); M. J. Englefield and C. Quesne, J. Phys. A24, 3557 (1991).
29. See, for example, B. G. Wybourne, Classical Groups for Physicists (Wiley-Interscience, New York, 1974), and references therein; W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Gürsey and F. Iachello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N.Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iachello and R. Levine, Phys. Rev. Lett. 54, 1746 (1985); Y. Alhassid, F. Iachello and J. Wu, Phys. Rev. Lett. 56, 271 (1986); J. Wu and Y. Alhassid, J. Math. Phys. 31, 557 (1990); M. J. Englefield and C. Quesne, J. Phys. A24, 3557 (1991).
30. A. de Souza-Dutra, Phys. Rev. A47, R2435 (1993); N. Nag, R. Roychoudhury and Y. P. Varshni, Phys. Rev. A49, 5098 (1994); R. Dutt, A. Khare and Y. P. Varshni, J. Phys. A28, L107 (1995); C. Grosche, J. Phys. A28, 5889 (1995); ibid. 29, 365 (1996); G. Lévai and P. Roy, Phys. Lett. A270, 155 (1998); G. Junker and P. Roy, Ann. Phys. (N. Y.) 264, 117 (1999); R. Roychoudhury, P. Roy, M. Zonjil and G. Lévai, J. Math. Phys. 42, 1996 (2001).
31. A. de Souza-Dutra, Phys. Rev. A47, R2435 (1993); N. Nag, R. Roychoudhury and Y. P. Varshni, Phys. Rev. A49, 5098 (1994); R. Dutt, A. Khare and Y. P. Varshni, J. Phys. A28, L107 (1995); C. Grosche, J. Phys. A28, 5889 (1995); ibid. 29, 365 (1996); G. Lévai and P. Roy, Phys. Lett. A270, 155 (1998); G. Junker and P. Roy, Ann. Phys. (N. Y.) 264, 117 (1999); R. Roychoudhury, P. Roy, M. Zonjil and G. Lévai, J. Math. Phys. 42, 1996 (2001).
32. A. de Souza-Dutra, Phys. Rev. A47, R2435 (1993); N. Nag, R. Roychoudhury and Y. P. Varshni, Phys. Rev. A49, 5098 (1994); R. Dutt, A. Khare and Y. P. Varshni, J. Phys. A28, L107 (1995); C. Grosche, J. Phys. A28, 5889 (1995); ibid. 29, 365 (1996); G. Lévai and P. Roy, Phys. Lett. A270, 155 (1998); G. Junker and P. Roy, Ann. Phys. (N. Y.) 264, 117 (1999); R. Roychoudhury, P. Roy, M. Zonjil and G. Lévai, J. Math. Phys. 42, 1996 (2001).
33. A. de Souza-Dutra, Phys. Rev. A47, R2435 (1993); N. Nag, R. Roychoudhury and Y. P. Varshni, Phys. Rev. A49, 5098 (1994); R. Dutt, A. Khare and Y. P. Varshni, J. Phys. A28, L107 (1995); C. Grosche, J. Phys. A28, 5889 (1995); ibid. 29, 365 (1996); G. Lévai and P. Roy, Phys. Lett. A270, 155 (1998); G. Junker and P. Roy, Ann. Phys. (N. Y.) 264, 117 (1999); R. Roychoudhury, P. Roy, M. Zonjil and G. Lévai, J. Math. Phys. 42, 1996 (2001).
34. A. de Souza-Dutra, Phys. Rev. A47, R2435 (1993); N. Nag, R. Roychoudhury and Y. P. Varshni, Phys. Rev. A49, 5098 (1994); R. Dutt, A. Khare and Y. P. Varshni, J. Phys. A28, L107 (1995); C. Grosche, J. Phys. A28, 5889 (1995); ibid. 29, 365 (1996); G. Lévai and P. Roy, Phys. Lett. A270, 155 (1998); G. Junker and P. Roy, Ann. Phys. (N. Y.) 264, 117 (1999); R. Roychoudhury, P. Roy, M. Zonjil and G. Lévai, J. Math. Phys. 42, 1996 (2001).
35. A. de Souza-Dutra, Phys. Rev. A47, R2435 (1993); N. Nag, R. Roychoudhury and Y. P. Varshni, Phys. Rev. A49, 5098 (1994); R. Dutt, A. Khare and Y. P. Varshni, J. Phys. A28, L107 (1995); C. Grosche, J. Phys. A28, 5889 (1995); ibid. 29, 365 (1996); G. Lévai and P. Roy, Phys. Lett. A270, 155 (1998); G. Junker and P. Roy, Ann. Phys. (N. Y.) 264, 117 (1999); R. Roychoudhury, P. Roy, M. Zonjil and G. Lévai, J. Math. Phys. 42, 1996 (2001).
36. A. de Souza-Dutra, Phys. Rev. A47, R2435 (1993); N. Nag, R. Roychoudhury and Y. P. Varshni, Phys. Rev. A49, 5098 (1994); R. Dutt, A. Khare and Y. P. Varshni, J. Phys. A28, L107 (1995); C. Grosche, J. Phys. A28, 5889 (1995); ibid. 29, 365 (1996); G. Lévai and P. Roy, Phys. Lett. A270, 155 (1998); G. Junker and P. Roy, Ann. Phys. (N. Y.) 264, 117 (1999); R. Roychoudhury, P. Roy, M. Zonjil and G. Lévai, J. Math. Phys. 42, 1996 (2001).
37. A. de Souza-Dutra, Phys. Rev. A47, R2435 (1993); N. Nag, R. Roychoudhury and Y. P. Varshni, Phys. Rev. A49, 5098 (1994); R. Dutt, A. Khare and Y. P. Varshni, J. Phys. A28, L107 (1995); C. Grosche, J. Phys. A28, 5889 (1995); ibid. 29, 365 (1996); G. Lévai and P. Roy, Phys. Lett. A270, 155 (1998); G. Junker and P. Roy, Ann. Phys. (N. Y.) 264, 117 (1999); R. Roychoudhury, P. Roy, M. Zonjil and G. Lévai, J. Math. Phys. 42, 1996 (2001).
38. A. V. Turbiner, Commun. Math. Phys. 118, 467 (1988); M. A. Shifman, Int. J. Mod. Phys. A4, 2897 (1989); R. Adhikari, R. Dutt and Y. Varshni, Phys. Lett. A141, 1 (1989); J. Math. Phys. 32, 447 (1991); R. K. Roychoudhury, Y. P. Varshni and M. Sengupta, Phys. Rev. A42, 184 (1990); L. D. Salem and R. Montemayor, Phys. Rev. A43, 1169 (1991); M. W. Lucht and P. D. Jarvis, Phys. Rev. A47, 817 (1993); A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1994).
39. A. V. Turbiner, Commun. Math. Phys. 118, 467 (1988); M. A. Shifman, Int. J. Mod. Phys. A4, 2897 (1989); R. Adhikari, R. Dutt and Y. Varshni, Phys. Lett. A141, 1 (1989); J. Math. Phys. 32, 447 (1991); R. K. Roychoudhury, Y. P. Varshni and M. Sengupta, Phys. Rev. A42, 184 (1990); L. D. Salem and R. Montemayor, Phys. Rev. A43, 1169 (1991); M. W. Lucht and P. D. Jarvis, Phys. Rev. A47, 817 (1993); A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1994).
40. A. V. Turbiner, Commun. Math. Phys. 118, 467 (1988); M. A. Shifman, Int. J. Mod. Phys. A4, 2897 (1989); R. Adhikari, R. Dutt and Y. Varshni, Phys. Lett. A141, 1 (1989); J. Math. Phys. 32, 447 (1991); R. K. Roychoudhury, Y. P. Varshni and M. Sengupta, Phys. Rev. A42, 184 (1990); L. D. Salem and R. Montemayor, Phys. Rev. A43, 1169 (1991); M. W. Lucht and P. D. Jarvis, Phys. Rev. A47, 817 (1993); A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1994).
41. A. V. Turbiner, Commun. Math. Phys. 118, 467 (1988); M. A. Shifman, Int. J. Mod. Phys. A4, 2897 (1989); R. Adhikari, R. Dutt and Y. Varshni, Phys. Lett. A141, 1 (1989); J. Math. Phys. 32, 447 (1991); R. K. Roychoudhury, Y. P. Varshni and M. Sengupta, Phys. Rev. A42, 184 (1990); L. D. Salem and R. Montemayor, Phys. Rev. A43, 1169 (1991); M. W. Lucht and P. D. Jarvis, Phys. Rev. A47, 817 (1993); A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1994).
42. A. V. Turbiner, Commun. Math. Phys. 118, 467 (1988); M. A. Shifman, Int. J. Mod. Phys. A4, 2897 (1989); R. Adhikari, R. Dutt and Y. Varshni, Phys. Lett. A141, 1 (1989); J. Math. Phys. 32, 447 (1991); R. K. Roychoudhury, Y. P. Varshni and M. Sengupta, Phys. Rev. A42, 184 (1990); L. D. Salem and R. Montemayor, Phys. Rev. A43, 1169 (1991); M. W. Lucht and P. D. Jarvis, Phys. Rev. A47, 817 (1993); A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1994).
43. A. V. Turbiner, Commun. Math. Phys. 118, 467 (1988); M. A. Shifman, Int. J. Mod. Phys. A4, 2897 (1989); R. Adhikari, R. Dutt and Y. Varshni, Phys. Lett. A141, 1 (1989); J. Math. Phys. 32, 447 (1991); R. K. Roychoudhury, Y. P. Varshni and M. Sengupta, Phys. Rev. A42, 184 (1990); L. D. Salem and R. Montemayor, Phys. Rev. A43, 1169 (1991); M. W. Lucht and P. D. Jarvis, Phys. Rev. A47, 817 (1993); A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1994).
44. A. V. Turbiner, Commun. Math. Phys. 118, 467 (1988); M. A. Shifman, Int. J. Mod. Phys. A4, 2897 (1989); R. Adhikari, R. Dutt and Y. Varshni, Phys. Lett. A141, 1 (1989); J. Math. Phys. 32, 447 (1991); R. K. Roychoudhury, Y. P. Varshni and M. Sengupta, Phys. Rev. A42, 184 (1990); L. D. Salem and R. Montemayor, Phys. Rev. A43, 1169 (1991); M. W. Lucht and P. D. Jarvis, Phys. Rev. A47, 817 (1993); A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1994).
45. A. V. Turbiner, Commun. Math. Phys. 118, 467 (1988); M. A. Shifman, Int. J. Mod. Phys. A4, 2897 (1989); R. Adhikari, R. Dutt and Y. Varshni, Phys. Lett. A141, 1 (1989); J. Math. Phys. 32, 447 (1991); R. K. Roychoudhury, Y. P. Varshni and M. Sengupta, Phys. Rev. A42, 184 (1990); L. D. Salem and R. Montemayor, Phys. Rev. A43, 1169 (1991); M. W. Lucht and P. D. Jarvis, Phys. Rev. A47, 817 (1993); A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (IOP, Bristol, 1994).
46. M. Moshinsky and A. Szczepaniak, J. Phys. A22, L817 (1989); J. Bentez, R. P. Martinez-y-Romero, H. N. Nunez-Yepez and A. L. Salas-Brito, Phys. Rev. Lett. 64, 1643 (1990); O. L. de Lange, J. Phys. A24, 667 (1991); V. M. Villalba, Phys. Rev. A49, 586 (1994); P. Rozmej and R. Arvieu, J. Phys. A32, 5367 (1999); R. Szmytkowski and M. Gruchowski, J. Phys. A34, 4991 (2001).
47. M. Moshinsky and A. Szczepaniak, J. Phys. A22, L817 (1989); J. Bentez, R. P. Martinez-y-Romero, H. N. Nunez-Yepez and A. L. Salas-Brito, Phys. Rev. Lett. 64, 1643 (1990); O. L. de Lange, J. Phys. A24, 667 (1991); V. M. Villalba, Phys. Rev. A49, 586 (1994); P. Rozmej and R. Arvieu, J. Phys. A32, 5367 (1999); R. Szmytkowski and M. Gruchowski, J. Phys. A34, 4991 (2001).
48. M. Moshinsky and A. Szczepaniak, J. Phys. A22, L817 (1989); J. Bentez, R. P. Martinez-y-Romero, H. N. Nunez-Yepez and A. L. Salas-Brito, Phys. Rev. Lett. 64, 1643 (1990); O. L. de Lange, J. Phys. A24, 667 (1991); V. M. Villalba, Phys. Rev. A49, 586 (1994); P. Rozmej and R. Arvieu, J. Phys. A32, 5367 (1999); R. Szmytkowski and M. Gruchowski, J. Phys. A34, 4991 (2001).
49. M. Moshinsky and A. Szczepaniak, J. Phys. A22, L817 (1989); J. Bentez, R. P. Martinez-y-Romero, H. N. Nunez-Yepez and A. L. Salas-Brito, Phys. Rev. Lett. 64, 1643 (1990); O. L. de Lange, J. Phys. A24, 667 (1991); V. M. Villalba, Phys. Rev. A49, 586 (1994); P. Rozmej and R. Arvieu, J. Phys. A32, 5367 (1999); R. Szmytkowski and M. Gruchowski, J. Phys. A34, 4991 (2001).
50. M. Moshinsky and A. Szczepaniak, J. Phys. A22, L817 (1989); J. Bentez, R. P. Martinez-y-Romero, H. N. Nunez-Yepez and A. L. Salas-Brito, Phys. Rev. Lett. 64, 1643 (1990); O. L. de Lange, J. Phys. A24, 667 (1991); V. M. Villalba, Phys. Rev. A49, 586 (1994); P. Rozmej and R. Arvieu, J. Phys. A32, 5367 (1999); R. Szmytkowski and M. Gruchowski, J. Phys. A34, 4991 (2001).
51. M. Moshinsky and A. Szczepaniak, J. Phys. A22, L817 (1989); J. Bentez, R. P. Martinez-y-Romero, H. N. Nunez-Yepez and A. L. Salas-Brito, Phys. Rev. Lett. 64, 1643 (1990); O. L. de Lange, J. Phys. A24, 667 (1991); V. M. Villalba, Phys. Rev. A49, 586 (1994); P. Rozmej and R. Arvieu, J. Phys. A32, 5367 (1999); R. Szmytkowski and M. Gruchowski, J. Phys. A34, 4991 (2001).
52. A. D. Alhaidari, Phys. Rev. Lett. 87, 210405 (2001); 88, 189901 (2002).
53. A. D. Alhaidari, Phys. Rev. Lett. 87, 210405 (2001); 88, 189901 (2002).
54. A. D. Alhaidari, J. Phys. A34, 9827 (2001); 35, 6207 (2002).
55. A. D. Alhaidari, J. Phys. A34, 9827 (2001); 35, 6207 (2002).
56. A. D. Alhaidari, Int. J. Mod. Phys. A17, 4551 (2002).
57. A. D. Alhaidari, Phys. Rev. A65, 042109 (2002);
58. 66, 019902 (2002).
59. A. N. Vaidya and R. de L. Rodrigues, Phys. Rev. Lett. 89, 068901 (2002).
60. A. S. de Castro, J. Phys. A35, 6203 (2002).
61. A. N. Vaidya and R. de L. Rodrigues, J. Phys. A35, 6205 (2002).
62. J.-Y. Guo, X. Z. Fang and F.-X. Xu, Phys. Rev. A66, 062105 (2002).
63. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1965).
64. A. D. Alhaidari, to be published; e-print hep-th/0207018.
65. W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd ed. (Springer-Verlag, New York, 1966).
66. R. De, R. Dutt and U. Sukhatme, J. Phys. A25, L843 (1992).
67. The expressions for the relativistic energy spectrum of the Dirac-Rosen-Morse I and Dirac-Eckart problems in Ref. 9 contain a typo. The correction is as shown here and in Table 1.
68. S. Flügge, Practical Quantum Mechanics (Springer-Verlag, Berlin, 1974), p. 165.