Non-Hermitian matrix description of the PT-symmetric anharmonic oscillators

Journal of Physics A: Mathematical and General

Volumn 32, Issue 42, 1999, Pages 7419-7428

  Znojil, Miloslav ^a  

^a NUCLEAR PHYSICS INSTITUTE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033595624     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/42/313     Document Type: Article

References (78)

1. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
2. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
3. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
4. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
5. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
6. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
7. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
8. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
9. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
10. Bender C M and Wu T T 1969 Phys. Rev. 184 1231 Killingbeck J 1980 J. Phys. A: Math. Gen. 13 49 Simon B 1982 Int. J. Quantum Chem. 21 3 Voros A 1983 Ann. Inst. Henri Poincaré A 39 211 Turbiner A V 1989 Sov. Sci. Rev. A: Phys. 10 79 Bender C M and Dunne G V 1989 Phys. Rev. D 40 3504 Kleinert H 1990 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (Singapore: World Scientific) Arponen J S and Bishop R F 1990 Phys. Rev. Lett. 64 111 Weniger E J 1996 Ann. Phys., NY 246 133 Lay W 1997 J. Math. Phys. 38 639
11. Bender C M and Boettcher S 1998 J. Phys. A: Math. Gen. 31 L273
12. Ushveridze A G 1994 Quasi-Exactly Solvable Models in Quantum Mechanics (Bristol: Institute of Physics Publishing)
13. Bessis D 1992 Private communication
14. Le Guillou J C and Zinn-Justin J (ed) 1990 Large-Order Behaviour of Perturbation Theory (Amsterdam: North Holland) Bender C M and Milton K A 1998 Phys. Rev. D 57 3595
15. Le Guillou J C and Zinn-Justin J (ed) 1990 Large-Order Behaviour of Perturbation Theory (Amsterdam: North Holland) Bender C M and Milton K A 1998 Phys. Rev. D 57 3595
16. Bishop R F, Flynn M F, Boscá M C and Guardiola R 1989 Phys. Rev. A 40 6154 Navrátil P, Geyer H B and Kuo T T S 1993 Phys. Lett. B 315 1
17. Bishop R F, Flynn M F, Boscá M C and Guardiola R 1989 Phys. Rev. A 40 6154 Navrátil P, Geyer H B and Kuo T T S 1993 Phys. Lett. B 315 1
18. Hatano N and Nelson D R 1996 Phys. Rev. Lett. 77 570 Bender C M, Dunne G V and Meisinger P N 1999 Phys. Lett. A 252 272 (Bender C M, Dunne G V and Meisinger P N 1998 Preprint cond-mat/9810369)
19. Hatano N and Nelson D R 1996 Phys. Rev. Lett. 77 570 Bender C M, Dunne G V and Meisinger P N 1999 Phys. Lett. A 252 272 (Bender C M, Dunne G V and Meisinger P N 1998 Preprint cond-mat/9810369)
20. Hatano N and Nelson D R 1996 Phys. Rev. Lett. 77 570 Bender C M, Dunne G V and Meisinger P N 1999 Phys. Lett. A 252 272 (Bender C M, Dunne G V and Meisinger P N 1998 Preprint cond-mat/9810369)
21. Cannata F, Junker G and Trost J 1998 Phys. Lett. A 246 219 Andrianov A A, Cannata F, Dedonder J P and Ioffe M V 1999 Int. J. Mod. Phys. A 14 2675 (Andrianov A A, Cannata F, Dedonder J P and Ioffe M V 1998 Preprint quant-ph/9806019)
22. Cannata F, Junker G and Trost J 1998 Phys. Lett. A 246 219 Andrianov A A, Cannata F, Dedonder J P and Ioffe M V 1999 Int. J. Mod. Phys. A 14 2675 (Andrianov A A, Cannata F, Dedonder J P and Ioffe M V 1998 Preprint quant-ph/9806019)
23. Cannata F, Junker G and Trost J 1998 Phys. Lett. A 246 219 Andrianov A A, Cannata F, Dedonder J P and Ioffe M V 1999 Int. J. Mod. Phys. A 14 2675 (Andrianov A A, Cannata F, Dedonder J P and Ioffe M V 1998 Preprint quant-ph/9806019)
24. Bender C M, Boettcher S and Meisinger P N 1999 J. Math. Phys. 40 2201 Fernández F, Guardiola R, Ros J and Znojil M 1999 J. Phys. A: Math. Gen. 32 3105
25. Bender C M, Boettcher S and Meisinger P N 1999 J. Math. Phys. 40 2201 Fernández F, Guardiola R, Ros J and Znojil M 1999 J. Phys. A: Math. Gen. 32 3105
26. Bender C M and Boettcher S 1998 Phys. Rev. Lett. 24 5243
27. Fernández F, Guardiola R, Ros J and Znojil M 1998 J. Phys. A: Math. Gen. 31 10 105 Bender C M and Dunne G V 1998 Preprint quant-ph/9812039
28. Fernández F, Guardiola R, Ros J and Znojil M 1998 J. Phys. A: Math. Gen. 31 10 105 Bender C M and Dunne G V 1998 Preprint quant-ph/9812039
29. Calicetti E, Graffi S and Maioli M 1980 Commun. Math. Phys. 75 51 Delabaere E and Pham F 1997 Ann. Phys. 261 180 Blencowe M P, Jones H and Korte A P 1998 Phys. Rev. D 57 5092
30. Calicetti E, Graffi S and Maioli M 1980 Commun. Math. Phys. 75 51 Delabaere E and Pham F 1997 Ann. Phys. 261 180 Blencowe M P, Jones H and Korte A P 1998 Phys. Rev. D 57 5092
31. Calicetti E, Graffi S and Maioli M 1980 Commun. Math. Phys. 75 51 Delabaere E and Pham F 1997 Ann. Phys. 261 180 Blencowe M P, Jones H and Korte A P 1998 Phys. Rev. D 57 5092
32. Bender C M and Turbiner A V 1993 Phys. Lett. A 173 442
33. Dyson F J 1952 Phys. Rev. 85 631
34. Bender C M and Milton K A 1999 J. Phys. A: Math. Gen. 32 L87
35. Alvarez G 1995 J. Phys. A: Math. Gen. 27 4589
36. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
37. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
38. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
39. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
40. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
41. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
42. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
43. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
44. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
45. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
46. Richardson J L and Blankenbecler R 1979 Phys. Rev. D 19 496 Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 Flessas G P and Watt A 1981 J. Phys. A: Math. Gen. 14 L315 Chaudhuri R N 1985 Phys. Rev. D 31 2687 Killingbeck J 1986 Phys. Lett. A 115 301 Bishop R F and Flynn M F 1988 Phys. Rev. A 38 2211 Hodgson R J W and Varshni Y P 1989 J. Phys. A: Math. Gen. 22 61 Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184 Bessis N and Bessis G 1997 J. Math. Phys. 38 5483 Sergeev A V and Goodson D Z 1998 J. Phys. A: Math. Gen. 31 4301 Skala L, Čížek J, Weniger E J and Zamastil J 1999 Phys. Rev. A 59 102
47. Ginsburg C A 1982 Phys. Rev. Lett. 48 839 Tater M 1987 J. Phys. A: Math. Gen. 20 2483
48. Ginsburg C A 1982 Phys. Rev. Lett. 48 839 Tater M 1987 J. Phys. A: Math. Gen. 20 2483
49. Estrin D A, Fernandez F M and Castro E A 1988 Phys. Lett. A 130 330 Znojil M 1991 Phys. Lett. A 155 83
50. Estrin D A, Fernandez F M and Castro E A 1988 Phys. Lett. A 130 330 Znojil M 1991 Phys. Lett. A 155 83
51. Singh V, Biswas S N and Data K 1978 Phys. Rev. D 18 1901
52. Cizek J and Vrscay E R 1984 Phys. Rev. A 30 1550
53. Lee M H 1982 Phys. Rev. B 26 2547
54. Masson D 1983 J. Math. Phys. 24 2974
55. Lakhtakia A 1989 J. Phys. A: Math. Gen. 22 1791
56. Arteca A G, Fernandez F M and Castro E A 1990 Large Order Perturbation Theory and Summation Methods in Quantum Mechanics (Berlin: Springer)
57. Meyer H-D, Horáček J and Cederbaum L S 1991 Phys. Rev. A 43 3587
58. Graffi S and Grecchi V 1975 Lett. Nuovo Cimento 12 425 Turchetti G 1978 Fortschr. Phys. 26 1 Znojil M 1988 J. Math. Phys. 29 139 Scherrer H. Risken H and Leiber T 1988 Phys. Rev. 38 3949 Ahlbrandt C D 1996. J. Approx. Theory 84 188
59. Graffi S and Grecchi V 1975 Lett. Nuovo Cimento 12 425 Turchetti G 1978 Fortschr. Phys. 26 1 Znojil M 1988 J. Math. Phys. 29 139 Scherrer H. Risken H and Leiber T 1988 Phys. Rev. 38 3949 Ahlbrandt C D 1996. J. Approx. Theory 84 188
60. Graffi S and Grecchi V 1975 Lett. Nuovo Cimento 12 425 Turchetti G 1978 Fortschr. Phys. 26 1 Znojil M 1988 J. Math. Phys. 29 139 Scherrer H. Risken H and Leiber T 1988 Phys. Rev. 38 3949 Ahlbrandt C D 1996. J. Approx. Theory 84 188
61. Graffi S and Grecchi V 1975 Lett. Nuovo Cimento 12 425 Turchetti G 1978 Fortschr. Phys. 26 1 Znojil M 1988 J. Math. Phys. 29 139 Scherrer H. Risken H and Leiber T 1988 Phys. Rev. 38 3949 Ahlbrandt C D 1996. J. Approx. Theory 84 188
62. Graffi S and Grecchi V 1975 Lett. Nuovo Cimento 12 425 Turchetti G 1978 Fortschr. Phys. 26 1 Znojil M 1988 J. Math. Phys. 29 139 Scherrer H. Risken H and Leiber T 1988 Phys. Rev. 38 3949 Ahlbrandt C D 1996. J. Approx. Theory 84 188
63. Znojil M 1994 J. Phys. A: Math. Gen. 27 4945
64. Birkhoff G D 1930 Acta Math. 54 205
65. Znojil M, Sandler K and Tater M 1985 J. Phys. A: Math. Gen. 18 2541
66. Bay K, Lay W and Akopyan A 1997 J. Phys. A: Math. Gen. 30 3057 and further references quoted therein
67. Znojil M 1988 J. Math. Phys. 29 1433
68. Hautot A 1986 Phys. Rev. D 33 437
69. Hille E 1969 Lectures on Ordinary Differential Equations (Reading, MA: Addison-Wesley)
70. Flügge S 1971 Practical Quantum Mechanics vol I (New York: Springer) p 153
71. Char B W et al 1991 Maple V Language Reference Manual (New York: Springer) Čížek J, Vinette F and Weniger E J 1991 Int. J. Quantum Chem. Quantum Chem. Symp. 25 209 de Groot R A and Nadrchal J (ed) 1993 Physics Computing '92 (Singapore: World Scientific) p 31
72. Char B W et al 1991 Maple V Language Reference Manual (New York: Springer) Čížek J, Vinette F and Weniger E J 1991 Int. J. Quantum Chem. Quantum Chem. Symp. 25 209 de Groot R A and Nadrchal J (ed) 1993 Physics Computing '92 (Singapore: World Scientific) p 31
73. Char B W et al 1991 Maple V Language Reference Manual (New York: Springer) Čížek J, Vinette F and Weniger E J 1991 Int. J. Quantum Chem. Quantum Chem. Symp. 25 209 de Groot R A and Nadrchal J (ed) 1993 Physics Computing '92 (Singapore: World Scientific) p 31
74. Fernandez FM 1991 Phys. Lett. A 160 116
75. Jaffé G 1933 Z. Phys. 87 535 Solov'ev E A 1981 Sov. Phys.-JETP 54 893
76. Jaffé G 1933 Z. Phys. 87 535 Solov'ev E A 1981 Sov. Phys.-JETP 54 893
77. Znojil M 1996 J. Phys. A: Math. Gen. 29 2905
78. Znojil M 1992 J. Math. Phys. 33 213