Two families of superintegrable and isospectral potentials in two dimensions

Journal of Mathematical Physics

Volumn 43, Issue 5, 2002, Pages 2133-2150

  Demircioglu, B ^a   Kuru, S ^a   Onder M ^b   Vercin A ^a  

^a ANKARA UNIVERSITY   (Turkey)

^b HACETTEPE UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035981792     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1463217     Document Type: Article

References (41)

1. V.I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed. (Springer, Bedim 1989).
2. H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading MA, 1980).
3. J. Fris, V. Mandrosov, Ya.A. Smorodinsky, M. Uhlir, and P. Winternitz, Phys. Lett. 16, 354 (1965); P. Winternitz, Ya.A. Smorodinsky, M. Uhlir, and J. Fris, Nucl. Phys. B 4, 444 (1967).
4. J. Fris, V. Mandrosov, Ya.A. Smorodinsky, M. Uhlir, and P. Winternitz, Phys. Lett. 16, 354 (1965); P. Winternitz, Ya.A. Smorodinsky, M. Uhlir, and J. Fris, Nucl. Phys. B 4, 444 (1967).
5. A. Makarov, Ya.A. Smorodinsky, Kh. Valiev, and P. Winternitz, Nuovo Cimento A 52, 1061 (1967).
6. S. Wojciechowski, Phys. Lett. 95A, 279 (1983).
7. N.W. Evans, Phys. Lett. A 147, 483 (1990).
8. N.W. Evans, Phys. Rev. A 41, 5666 (1990); J. Math. Phys. 32, 3369 (1991).
9. N.W. Evans, Phys. Rev. A 41, 5666 (1990); J. Math. Phys. 32, 3369 (1991).
10. C. Grosche, G.S. Pogosyan, and A.N. Sissakian, Fortschr. Phys. 43, 453 (1995).
11. M.F. Ramada, J. Math. Phys. 38, 4165 (1997).
12. M.B. Sheftel, P. Tempesta, and P. Winternitz, J. Math. Phys. 42, 659 (2001).
13. P. Tempesta, A.V. Turbiner, and P. Winternitz, J. Math. Phys. 42, 4248 (2001).
14. G. Junker, Supersymmetric Methods in Quantum and Statistical Physics (Springer, Berlin, 1996).
15. F. Cooper, A. Khare, and U. Sukhatme, Phys. Rep. 251, 267 (1995).
16. V.B. Matveev and M.A. Salle, Darboux Transformations and Solitons (Springer, Berlin, 1991).
17. Supersymmetry and Integrable Models, edited by H. Aratyn, T.D. Imbo, W.Y. Keung, and U. Sukhatme (Springer, Berlin, 1998).
18. A. Anderson, Phys. Rev. D 37, 536 (1989); A. Anderson and R. Camproesi, Commun. Math. Phys. 130, 61 (1990).
19. A. Anderson, Phys. Rev. D 37, 536 (1989); A. Anderson and R. Camproesi, Commun. Math. Phys. 130, 61 (1990).
20. F. Cannata, M. Ioffe, G. Junker, and D. Nishnianidzev, J. Phys. A 32, 3583 (1998).
21. A. Anderson, Phys. Rev. A 43, 4602 (1991).
22. R. Richtmyer, Principles of Advanced Mathematical Physics, Volume I, (Springer, Berlin, 1978).
23. T. Kato, Perturbation, Theory for Linear Operators, 2nd ed. (Springer, Berlin, 1980).
24. M. Reed and B. Simon, Method of the Modern Mathematical Physics (Springer, Berlin, 1980), Vols. I and II.
25. P.A. Deift, Duke Math. J. 45, 267 (1978).
26. D.L. Pursey, Phys. Rev. D 33, 2267 (1986).
27. W. Miller, Jr., Symmetry and Separation of Variables (Addison-Wesley, Reading, MA, 1977).
28. A. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin, 1986).
29. L. Lathouvers, J. Math. Phys. 16, 1393 (1975).
30. J. Fuchs, J. Math. Phys. 27, 349 (1986).
31. W. Magnus, F. Oberhettinger, and R. Soni, Formulas and Theorem for Special Functions of Mathematical Physics (Springer, New York, 1966).
32. P. Létourneau and L. Vinet, Ann. Phys. (N.Y.) 16, 349 (1995).
33. S. Flügge, Practical Quantum Mechanics (Springer, Berlin, 1974).
34. C. Daskaloyannis, J. Math. Phys. 42, 1100 (2001).
35. S.P. Novikov and A.P. Veselov, Am. Math. Soc. Trans. 179, 109 (1997); E.V. Ferapontov and A.P. Veselov, J. Math. Phys. 42, 590 (2001).
36. S.P. Novikov and A.P. Veselov, Am. Math. Soc. Trans. 179, 109 (1997); E.V. Ferapontov and A.P. Veselov, J. Math. Phys. 42, 590 (2001).
37. A.A. Andrianov, M.V. Ioffe, and D.N. Nishnianidze, Theor. Math. Phys. 104, 1129 (1995); Phys. Lett. A 201, 103 (1995).
38. A.A. Andrianov, M.V. Ioffe, and D.N. Nishnianidze, Theor. Math. Phys. 104, 1129 (1995); Phys. Lett. A 201, 103 (1995).
39. V.G. Bagrov and B.F. Samsonov, Phys. Lett. A 210, 60 (1996); F. Finkel, A.G. Lopez, N. Kamran, and M.A. Rodriguez, J. Math. Phys. 40, 3268 (1999).
40. V.G. Bagrov and B.F. Samsonov, Phys. Lett. A 210, 60 (1996); F. Finkel, A.G. Lopez, N. Kamran, and M.A. Rodriguez, J. Math. Phys. 40, 3268 (1999).
41. Ş. Kuru, A. Tegmen, and A. Verçin, J. Math. Phys. 42, 3344 (2001).