rD oscillators with arbitrary D>0 and perturbation expansions with Sturmians

Journal of Mathematical Physics

Volumn 38, Issue 10, 1997, Pages 5087-5097

  Znojil, Miloslav ^a  

^a NUCLEAR PHYSICS INSTITUTE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031533680     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531932     Document Type: Article

References (47)

1. A. Messiah, Quantum Mechanics (North Holland, Amsterdam, 1961); J. O. Hirschfelder, W. Byers-Brown, and S. T. Epstein, Adv. Quant. Chem. 1, 256 (1964); B. Simon, Bull. Am. Math. Soc. 24, 303 (1991).
2. A. Messiah, Quantum Mechanics (North Holland, Amsterdam, 1961); J. O. Hirschfelder, W. Byers-Brown, and S. T. Epstein, Adv. Quant. Chem. 1, 256 (1964); B. Simon, Bull. Am. Math. Soc. 24, 303 (1991).
3. A. Messiah, Quantum Mechanics (North Holland, Amsterdam, 1961); J. O. Hirschfelder, W. Byers-Brown, and S. T. Epstein, Adv. Quant. Chem. 1, 256 (1964); B. Simon, Bull. Am. Math. Soc. 24, 303 (1991).
4. C. Quigg and J. L. Rosner, Phys. Rep. 56, 167 (1979); V. C. Aguilera-Navarro, F. M. Fernández, R. Guardiola, and J. Ros, J. Phys. A: Math. Gen. 25, 6379 (1992); E. D. Filho, Mod. Phys. Lett. A 11, 207 (1996).
5. C. Quigg and J. L. Rosner, Phys. Rep. 56, 167 (1979); V. C. Aguilera-Navarro, F. M. Fernández, R. Guardiola, and J. Ros, J. Phys. A: Math. Gen. 25, 6379 (1992); E. D. Filho, Mod. Phys. Lett. A 11, 207 (1996).
6. C. Quigg and J. L. Rosner, Phys. Rep. 56, 167 (1979); V. C. Aguilera-Navarro, F. M. Fernández, R. Guardiola, and J. Ros, J. Phys. A: Math. Gen. 25, 6379 (1992); E. D. Filho, Mod. Phys. Lett. A 11, 207 (1996).
7. B. Simon, Int. J. Quant. Chem. 21, 3 (1982); D. A. Estrín, F. M. Fernández, and E. A. Cástro, Phys. Lett. A 130, 330 (1988); M. Bansal, S. Srivastava, X. Mamta, and X. Vishvamittar, Chem. Phys. Lett. 195, 505 (1992).
8. B. Simon, Int. J. Quant. Chem. 21, 3 (1982); D. A. Estrín, F. M. Fernández, and E. A. Cástro, Phys. Lett. A 130, 330 (1988); M. Bansal, S. Srivastava, X. Mamta, and X. Vishvamittar, Chem. Phys. Lett. 195, 505 (1992).
9. B. Simon, Int. J. Quant. Chem. 21, 3 (1982); D. A. Estrín, F. M. Fernández, and E. A. Cástro, Phys. Lett. A 130, 330 (1988); M. Bansal, S. Srivastava, X. Mamta, and X. Vishvamittar, Chem. Phys. Lett. 195, 505 (1992).
10. R. J. W. Hodgson and Y. P. Varshni, J. Phys. A: Math. Gen. 22, 61 (1989); F. Arias de Saavedra and E. Buendía, Phys. Rev. A 42, 5073 (1990); M. R. M. Witwit, J. Comput. Appl. Math. 67, 129 (1996).
11. R. J. W. Hodgson and Y. P. Varshni, J. Phys. A: Math. Gen. 22, 61 (1989); F. Arias de Saavedra and E. Buendía, Phys. Rev. A 42, 5073 (1990); M. R. M. Witwit, J. Comput. Appl. Math. 67, 129 (1996).
12. R. J. W. Hodgson and Y. P. Varshni, J. Phys. A: Math. Gen. 22, 61 (1989); F. Arias de Saavedra and E. Buendía, Phys. Rev. A 42, 5073 (1990); M. R. M. Witwit, J. Comput. Appl. Math. 67, 129 (1996).
13. K. Banerjee and S. P. Bhatnagar, Phys. Rev. D 18, 4767 (1978); L. H. Ryder, Quantum Field Theory (Cambridge U.P., Cambridge, 1985), Chap. VIII and Fig. 8.3.
14. K. Banerjee and S. P. Bhatnagar, Phys. Rev. D 18, 4767 (1978); L. H. Ryder, Quantum Field Theory (Cambridge U.P., Cambridge, 1985), Chap. VIII and Fig. 8.3.
15. W. E. Caswell, Ann. Phys. 123, 153 (1979); J. C. Le Gillou and J. Zinn-Justin, editors, Large-Order Behaviour of Perturbation Theory (North Holland, Amsterdam, 1990); E. J. Weniger, J. Čížek, and F. Vinette, J. Math. Phys. 34, 571 (1993).
16. W. E. Caswell, Ann. Phys. 123, 153 (1979); J. C. Le Gillou and J. Zinn-Justin, editors, Large-Order Behaviour of Perturbation Theory (North Holland, Amsterdam, 1990); E. J. Weniger, J. Čížek, and F. Vinette, J. Math. Phys. 34, 571 (1993).
17. W. E. Caswell, Ann. Phys. 123, 153 (1979); J. C. Le Gillou and J. Zinn-Justin, editors, Large-Order Behaviour of Perturbation Theory (North Holland, Amsterdam, 1990); E. J. Weniger, J. Čížek, and F. Vinette, J. Math. Phys. 34, 571 (1993).
18. J. M. Irvine, Nuclear Structure Theory (Pergamon, Oxford, 1972); J. W. Negele and H. Orland, Quantum Many-Particle Systems (Addison-Wesley, Reading, MA, 1988).
19. J. M. Irvine, Nuclear Structure Theory (Pergamon, Oxford, 1972); J. W. Negele and H. Orland, Quantum Many-Particle Systems (Addison-Wesley, Reading, MA, 1988).
20. S. Graffi, V. Grecchi, and B. Simon, Phys. Lett. B 32; 631 (1970); C. Brezinski and M. Redivo Zaglia, Extrapolation Methods (North Holland, Amsterdam, 1991); E. J. Weniger, Ann. Phys. 246, 133 (1996); C. M. Bender and J. P. Vinson, J. Math. Phys. 37, 4103 (1996).
21. S. Graffi, V. Grecchi, and B. Simon, Phys. Lett. B 32; 631 (1970); C. Brezinski and M. Redivo Zaglia, Extrapolation Methods (North Holland, Amsterdam, 1991); E. J. Weniger, Ann. Phys. 246, 133 (1996); C. M. Bender and J. P. Vinson, J. Math. Phys. 37, 4103 (1996).
22. S. Graffi, V. Grecchi, and B. Simon, Phys. Lett. B 32; 631 (1970); C. Brezinski and M. Redivo Zaglia, Extrapolation Methods (North Holland, Amsterdam, 1991); E. J. Weniger, Ann. Phys. 246, 133 (1996); C. M. Bender and J. P. Vinson, J. Math. Phys. 37, 4103 (1996).
23. S. Graffi, V. Grecchi, and B. Simon, Phys. Lett. B 32; 631 (1970); C. Brezinski and M. Redivo Zaglia, Extrapolation Methods (North Holland, Amsterdam, 1991); E. J. Weniger, Ann. Phys. 246, 133 (1996); C. M. Bender and J. P. Vinson, J. Math. Phys. 37, 4103 (1996).
24. I. G. Halliday and P. Suranyi, Phys. Rev. D 21, 1529 (1980).
25. I. D. Ferranchuk, L. I. Komarov, I. V. Nichipor, and A. P. Ulyanenko, Ann. Phys. (NY) 238, 370 (1995); H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, 1995); R. Guida, K. Konishi, and H. Suzuki, Ann. Phys. 241, 152 (1995); S. A. Pernice and G. Oleaga, "On the divergence of perturbation theory" (lecture in Cargese, September 1996, not yet published).
26. I. D. Ferranchuk, L. I. Komarov, I. V. Nichipor, and A. P. Ulyanenko, Ann. Phys. (NY) 238, 370 (1995); H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, 1995); R. Guida, K. Konishi, and H. Suzuki, Ann. Phys. 241, 152 (1995); S. A. Pernice and G. Oleaga, "On the divergence of perturbation theory" (lecture in Cargese, September 1996, not yet published).
27. I. D. Ferranchuk, L. I. Komarov, I. V. Nichipor, and A. P. Ulyanenko, Ann. Phys. (NY) 238, 370 (1995); H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, 1995); R. Guida, K. Konishi, and H. Suzuki, Ann. Phys. 241, 152 (1995); S. A. Pernice and G. Oleaga, "On the divergence of perturbation theory" (lecture in Cargese, September 1996, not yet published).
28. I. D. Ferranchuk, L. I. Komarov, I. V. Nichipor, and A. P. Ulyanenko, Ann. Phys. (NY) 238, 370 (1995); H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, 1995); R. Guida, K. Konishi, and H. Suzuki, Ann. Phys. 241, 152 (1995); S. A. Pernice and G. Oleaga, "On the divergence of perturbation theory" (lecture in Cargese, September 1996, not yet published).
29. R. Sternheimer, Phys. Rev. 84, 244 (1951); P. H. Price, Proc. Phys. Soc. London 67, 383 (1954); A. Dalgarno and J. T. Lewis, Proc. R. Soc. London 233, 70 (1955); Ia. B. Zel'dovich, Sov. Phys. JETP 4, 942 (1957); A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988); H. A. Mavromatis, Am. J. Phys. 59, 738 (1991); I.-W. Kim and U. P. Sukhatme, J. Phys. A: Math. Gen. 25, L647 (1992); T. K. Nandi, P. K. Bera, M. M. Panja, and B. Talukdar, J. Phys. A: Math. Gen. 29, 1101 (1996); L. Skála and J. Čížek, J. Phys. A: Math. Gen. 29, L129 (1996).
30. R. Sternheimer, Phys. Rev. 84, 244 (1951); P. H. Price, Proc. Phys. Soc. London 67, 383 (1954); A. Dalgarno and J. T. Lewis, Proc. R. Soc. London 233, 70 (1955); Ia. B. Zel'dovich, Sov. Phys. JETP 4, 942 (1957); A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988); H. A. Mavromatis, Am. J. Phys. 59, 738 (1991); I.-W. Kim and U. P. Sukhatme, J. Phys. A: Math. Gen. 25, L647 (1992); T. K. Nandi, P. K. Bera, M. M. Panja, and B. Talukdar, J. Phys. A: Math. Gen. 29, 1101 (1996); L. Skála and J. Čížek, J. Phys. A: Math. Gen. 29, L129 (1996).
31. R. Sternheimer, Phys. Rev. 84, 244 (1951); P. H. Price, Proc. Phys. Soc. London 67, 383 (1954); A. Dalgarno and J. T. Lewis, Proc. R. Soc. London 233, 70 (1955); Ia. B. Zel'dovich, Sov. Phys. JETP 4, 942 (1957); A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988); H. A. Mavromatis, Am. J. Phys. 59, 738 (1991); I.-W. Kim and U. P. Sukhatme, J. Phys. A: Math. Gen. 25, L647 (1992); T. K. Nandi, P. K. Bera, M. M. Panja, and B. Talukdar, J. Phys. A: Math. Gen. 29, 1101 (1996); L. Skála and J. Čížek, J. Phys. A: Math. Gen. 29, L129 (1996).
32. R. Sternheimer, Phys. Rev. 84, 244 (1951); P. H. Price, Proc. Phys. Soc. London 67, 383 (1954); A. Dalgarno and J. T. Lewis, Proc. R. Soc. London 233, 70 (1955); Ia. B. Zel'dovich, Sov. Phys. JETP 4, 942 (1957); A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988); H. A. Mavromatis, Am. J. Phys. 59, 738 (1991); I.-W. Kim and U. P. Sukhatme, J. Phys. A: Math. Gen. 25, L647 (1992); T. K. Nandi, P. K. Bera, M. M. Panja, and B. Talukdar, J. Phys. A: Math. Gen. 29, 1101 (1996); L. Skála and J. Čížek, J. Phys. A: Math. Gen. 29, L129 (1996).
33. R. Sternheimer, Phys. Rev. 84, 244 (1951); P. H. Price, Proc. Phys. Soc. London 67, 383 (1954); A. Dalgarno and J. T. Lewis, Proc. R. Soc. London 233, 70 (1955); Ia. B. Zel'dovich, Sov. Phys. JETP 4, 942 (1957); A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988); H. A. Mavromatis, Am. J. Phys. 59, 738 (1991); I.-W. Kim and U. P. Sukhatme, J. Phys. A: Math. Gen. 25, L647 (1992); T. K. Nandi, P. K. Bera, M. M. Panja, and B. Talukdar, J. Phys. A: Math. Gen. 29, 1101 (1996); L. Skála and J. Čížek, J. Phys. A: Math. Gen. 29, L129 (1996).
34. R. Sternheimer, Phys. Rev. 84, 244 (1951); P. H. Price, Proc. Phys. Soc. London 67, 383 (1954); A. Dalgarno and J. T. Lewis, Proc. R. Soc. London 233, 70 (1955); Ia. B. Zel'dovich, Sov. Phys. JETP 4, 942 (1957); A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988); H. A. Mavromatis, Am. J. Phys. 59, 738 (1991); I.-W. Kim and U. P. Sukhatme, J. Phys. A: Math. Gen. 25, L647 (1992); T. K. Nandi, P. K. Bera, M. M. Panja, and B. Talukdar, J. Phys. A: Math. Gen. 29, 1101 (1996); L. Skála and J. Čížek, J. Phys. A: Math. Gen. 29, L129 (1996).
35. R. Sternheimer, Phys. Rev. 84, 244 (1951); P. H. Price, Proc. Phys. Soc. London 67, 383 (1954); A. Dalgarno and J. T. Lewis, Proc. R. Soc. London 233, 70 (1955); Ia. B. Zel'dovich, Sov. Phys. JETP 4, 942 (1957); A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988); H. A. Mavromatis, Am. J. Phys. 59, 738 (1991); I.-W. Kim and U. P. Sukhatme, J. Phys. A: Math. Gen. 25, L647 (1992); T. K. Nandi, P. K. Bera, M. M. Panja, and B. Talukdar, J. Phys. A: Math. Gen. 29, 1101 (1996); L. Skála and J. Čížek, J. Phys. A: Math. Gen. 29, L129 (1996).
36. R. Sternheimer, Phys. Rev. 84, 244 (1951); P. H. Price, Proc. Phys. Soc. London 67, 383 (1954); A. Dalgarno and J. T. Lewis, Proc. R. Soc. London 233, 70 (1955); Ia. B. Zel'dovich, Sov. Phys. JETP 4, 942 (1957); A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988); H. A. Mavromatis, Am. J. Phys. 59, 738 (1991); I.-W. Kim and U. P. Sukhatme, J. Phys. A: Math. Gen. 25, L647 (1992); T. K. Nandi, P. K. Bera, M. M. Panja, and B. Talukdar, J. Phys. A: Math. Gen. 29, 1101 (1996); L. Skála and J. Čížek, J. Phys. A: Math. Gen. 29, L129 (1996).
37. R. Sternheimer, Phys. Rev. 84, 244 (1951); P. H. Price, Proc. Phys. Soc. London 67, 383 (1954); A. Dalgarno and J. T. Lewis, Proc. R. Soc. London 233, 70 (1955); Ia. B. Zel'dovich, Sov. Phys. JETP 4, 942 (1957); A. V. Turbiner and A. G. Ushveridze, J. Math. Phys. 29, 2053 (1988); H. A. Mavromatis, Am. J. Phys. 59, 738 (1991); I.-W. Kim and U. P. Sukhatme, J. Phys. A: Math. Gen. 25, L647 (1992); T. K. Nandi, P. K. Bera, M. M. Panja, and B. Talukdar, J. Phys. A: Math. Gen. 29, 1101 (1996); L. Skála and J. Čížek, J. Phys. A: Math. Gen. 29, L129 (1996).
38. I. S. Gradshteyn and I. M Ryzhik, Tables of Integrals, Sums, Series and Products (Nauka, Moscow, 1971).
39. F. Cooper, A. Khare, and U. Sukhatme, Phys. Rep. 251, 267 (1995).
40. J. Liouville, J. Math. Pures Appl. 1, 16 (1837); F. W. J. Olver, Introduction to Asympotics and Special Functions (Academic, New York, 1974), Chap. 6.
41. J. Liouville, J. Math. Pures Appl. 1, 16 (1837); F. W. J. Olver, Introduction to Asympotics and Special Functions (Academic, New York, 1974), Chap. 6.
42. T. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, Berlin, 1966).
43. F. Constantinescu and E. Magyari, Problems in Quantum Mechanics (Pergamon, Oxford, 1971).
44. B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, First Leaves: A Tutorial Introduction to Maple V (Springer-Verlag, New York, 1992).
45. A. N. Drozdov, J. Phys. A: Math. Gen. 28, 445 (1995).
46. W. Greiner and B. Müller, Gauge Theory of Weak Interactions (Springer-Verlag, Berlin, 1993), p. 261.
47. R. R. Whitehead, A. Watt, G. P. Flessas, and M. A. Nagarajan, J. Phys. A: Math. Gen. 15, 1217 (1982).