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Volumn 17, Issue 30, 2002, Pages 4551-4566

Exact solutions of Dirac and Schrödinger equations for a large class of power-law potentials at zero energy

Author keywords

Dirac equation; Exact solutions; Point canonical transformations; Power law potentials; So(2, 1) algebra; Zero energy

Indexed keywords

ARTICLE; ENERGY; MATHEMATICS; OSCILLATOR; PHYSICS;

EID: 0037058817     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X02010911     Document Type: Article
Times cited : (27)

References (75)
  • 1
    • 0001627532 scopus 로고    scopus 로고
    • J. Daboul and M. M. Nieto, Phys. Lett. A190, 357 (1994); Int. J. Mod. Phys. All, 3801 (1996).
    • (1994) Phys. Lett. , vol.A190 , pp. 357
    • Daboul, J.1    Nieto, M.M.2
  • 2
    • 0001627532 scopus 로고    scopus 로고
    • J. Daboul and M. M. Nieto, Phys. Lett. A190, 357 (1994); Int. J. Mod. Phys. All, 3801 (1996).
    • (1996) Int. J. Mod. Phys. , vol.A11 , pp. 3801
  • 4
    • 0003103780 scopus 로고    scopus 로고
    • B. Bagchi and C. Quesne, Phys. Lett. A230, 1 (1997); M. M. Nieto, Phys. Lett. B486, 414 (2000).
    • (1997) Phys. Lett. , vol.A230 , pp. 1
    • Bagchi, B.1    Quesne, C.2
  • 5
    • 0034601351 scopus 로고    scopus 로고
    • B. Bagchi and C. Quesne, Phys. Lett. A230, 1 (1997); M. M. Nieto, Phys. Lett. B486, 414 (2000).
    • (2000) Phys. Lett. , vol.B486 , pp. 414
    • Nieto, M.M.1
  • 6
    • 2742571438 scopus 로고
    • 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).
    • (1981) Nucl. Phys. , vol.B185 , pp. 513
    • Witten, E.1
  • 7
    • 0000767375 scopus 로고
    • 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).
    • (1983) Ann. Phys. (N. Y.) , vol.146 , pp. 262
    • Cooper, F.1    Freedman, B.2
  • 8
    • 0040182361 scopus 로고
    • 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).
    • (1985) J. Phys. , vol.A18 , pp. 2917
    • Sukumar, C.V.1
  • 9
    • 0000559352 scopus 로고
    • 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).
    • (1989) J. Math. Phys. , vol.30 , pp. 1164
    • Arai, A.1
  • 11
    • 0000791340 scopus 로고    scopus 로고
    • 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).
    • (1993) Phys. Rev. , vol.A47
    • De Souza-Dutra, A.1
  • 12
    • 0001241144 scopus 로고
    • 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).
    • (1994) Phys. Rev. , vol.A49 , pp. 5098
    • Nag, N.1    Roychoudhury, R.2    Varshni, Y.P.3
  • 13
    • 21844513243 scopus 로고
    • 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).
    • (1995) J. Phys. , vol.A28
    • Dutt, R.1    Khare, A.2    Varshni, Y.P.3
  • 14
    • 21844485156 scopus 로고
    • 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).
    • (1995) J. Phys. , vol.A28 , pp. 5889
    • Grosche, C.1
  • 15
    • 0000791340 scopus 로고    scopus 로고
    • 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).
    • (1996) J. Phys. , vol.29 , pp. 365
  • 16
    • 0000791340 scopus 로고    scopus 로고
    • 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).
    • (1998) Phys. Lett. , vol.A270 , pp. 155
    • Lévai, G.1    Roy, P.2
  • 17
    • 0000791340 scopus 로고    scopus 로고
    • 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).
    • (1999) Ann. Phys. (N. Y.) , vol.264 , pp. 117
    • Junker, G.1    Roy, P.2
  • 18
    • 0035532243 scopus 로고    scopus 로고
    • 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).
    • (2001) J. Math. Phys. , vol.42 , pp. 1996
    • Roychoudhury, R.1    Roy, P.2    Zonjil, M.3    Lévai, G.4
  • 19
    • 0009491906 scopus 로고
    • 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).
    • (1988) Commun. Math. Phys. , vol.118 , pp. 467
    • Turbiner, A.V.1
  • 20
    • 0000999213 scopus 로고
    • 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).
    • (1989) Int. J. Mod. Phys. , vol.A4 , pp. 2897
    • Shifman, M.A.1
  • 21
    • 0002484767 scopus 로고
    • 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).
    • (1989) Phys. Lett. , vol.A141 , pp. 1
    • Adhikari, R.1    Dutt, R.2    Varshni, Y.3
  • 22
    • 22244485630 scopus 로고
    • 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).
    • (1991) J. Math. Phys. , vol.32 , pp. 447
  • 23
    • 0001448786 scopus 로고
    • 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).
    • (1990) Phys. Rev. , vol.A42 , pp. 184
    • Roychoudhury, R.K.1    Varshni, Y.P.2    Sengupta, M.3
  • 24
    • 0001583338 scopus 로고
    • 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).
    • (1991) Phys. Rev. , vol.A43 , pp. 1169
    • Salem, L.D.1    Montemayor, R.2
  • 25
    • 0000144729 scopus 로고
    • 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).
    • (1993) Phys. Rev. , vol.A47 , pp. 817
    • Lucht, M.W.1    Jarvis, P.D.2
  • 26
    • 0004104648 scopus 로고
    • IOP, Bristol
    • 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).
    • (1994) Quasi-Exactly Solvable Models in Quantum Mechanics
    • Ushveridze, A.G.1
  • 27
    • 0012003148 scopus 로고
    • B. W. Downs, Am. J. Phys. 30, 248 (1962); L. I. Schiff, Quantum Mechanics, 3rd Ed. (McGraw-Hill, New York, 1968); B. Bagchi, B. Mulligan and S. B. Qadri, Prog. Theor. Phys. 60, 765 (1978); A. O. Barut, J. Math. Phys. 21, 568 (1980).
    • (1962) Am. J. Phys. , vol.30 , pp. 248
    • Downs, B.W.1
  • 28
    • 0012003148 scopus 로고
    • McGraw-Hill, New York
    • B. W. Downs, Am. J. Phys. 30, 248 (1962); L. I. Schiff, Quantum Mechanics, 3rd Ed. (McGraw-Hill, New York, 1968); B. Bagchi, B. Mulligan and S. B. Qadri, Prog. Theor. Phys. 60, 765 (1978); A. O. Barut, J. Math. Phys. 21, 568 (1980).
    • (1968) Quantum Mechanics, 3rd Ed.
    • Schiff, L.I.1
  • 29
    • 0012003148 scopus 로고
    • B. W. Downs, Am. J. Phys. 30, 248 (1962); L. I. Schiff, Quantum Mechanics, 3rd Ed. (McGraw-Hill, New York, 1968); B. Bagchi, B. Mulligan and S. B. Qadri, Prog. Theor. Phys. 60, 765 (1978); A. O. Barut, J. Math. Phys. 21, 568 (1980).
    • (1978) Prog. Theor. Phys. , vol.60 , pp. 765
    • Bagchi, B.1    Mulligan, B.2    Qadri, S.B.3
  • 30
    • 36749112652 scopus 로고
    • B. W. Downs, Am. J. Phys. 30, 248 (1962); L. I. Schiff, Quantum Mechanics, 3rd Ed. (McGraw-Hill, New York, 1968); B. Bagchi, B. Mulligan and S. B. Qadri, Prog. Theor. Phys. 60, 765 (1978); A. O. Barut, J. Math. Phys. 21, 568 (1980).
    • (1980) J. Math. Phys. , vol.21 , pp. 568
    • Barut, A.O.1
  • 31
    • 0003405945 scopus 로고
    • Academic, New York
    • S. Gelman, Topics in Atomic Collision Theory (Academic, New York, 1969); B. H. Bransden, Atomic Collision Theory (W. A. Benjamin, New York, 1970); P. G. Burke, Potential Scattering in Atomic Physics (Plenum, New York, 1977); Yu. N. Demkov and G. F. Drukarev, Z. Eksp. i Teor. Fiz. 81, 1218 (1981); F. M. Toyama and Y. Nogami, Phys. Rev. C38, 2881 (1988); B. N. Zakhariev and A. A. Suzko, Direct and Inverse Problems: Potentials in Quantum Scattering (Springer-Verlag, Berlin, 1990).
    • (1969) Topics in Atomic Collision Theory
    • Gelman, S.1
  • 32
    • 0004267371 scopus 로고
    • W. A. Benjamin, New York
    • S. Gelman, Topics in Atomic Collision Theory (Academic, New York, 1969); B. H. Bransden, Atomic Collision Theory (W. A. Benjamin, New York, 1970); P. G. Burke, Potential Scattering in Atomic Physics (Plenum, New York, 1977); Yu. N. Demkov and G. F. Drukarev, Z. Eksp. i Teor. Fiz. 81, 1218 (1981); F. M. Toyama and Y. Nogami, Phys. Rev. C38, 2881 (1988); B. N. Zakhariev and A. A. Suzko, Direct and Inverse Problems: Potentials in Quantum Scattering (Springer-Verlag, Berlin, 1990).
    • (1970) Atomic Collision Theory
    • Bransden, B.H.1
  • 33
    • 0003740969 scopus 로고
    • Plenum, New York
    • S. Gelman, Topics in Atomic Collision Theory (Academic, New York, 1969); B. H. Bransden, Atomic Collision Theory (W. A. Benjamin, New York, 1970); P. G. Burke, Potential Scattering in Atomic Physics (Plenum, New York, 1977); Yu. N. Demkov and G. F. Drukarev, Z. Eksp. i Teor. Fiz. 81, 1218 (1981); F. M. Toyama and Y. Nogami, Phys. Rev. C38, 2881 (1988); B. N. Zakhariev and A. A. Suzko, Direct and Inverse Problems: Potentials in Quantum Scattering (Springer-Verlag, Berlin, 1990).
    • (1977) Potential Scattering in Atomic Physics
    • Burke, P.G.1
  • 34
    • 0012003149 scopus 로고
    • S. Gelman, Topics in Atomic Collision Theory (Academic, New York, 1969); B. H. Bransden, Atomic Collision Theory (W. A. Benjamin, New York, 1970); P. G. Burke, Potential Scattering in Atomic Physics (Plenum, New York, 1977); Yu. N. Demkov and G. F. Drukarev, Z. Eksp. i Teor. Fiz. 81, 1218 (1981); F. M. Toyama and Y. Nogami, Phys. Rev. C38, 2881 (1988); B. N. Zakhariev and A. A. Suzko, Direct and Inverse Problems: Potentials in Quantum Scattering (Springer-Verlag, Berlin, 1990).
    • (1981) Z. Eksp. i Teor. Fiz. , vol.81 , pp. 1218
    • Demkov, Yu.N.1    Drukarev, G.F.2
  • 35
    • 0011930661 scopus 로고
    • S. Gelman, Topics in Atomic Collision Theory (Academic, New York, 1969); B. H. Bransden, Atomic Collision Theory (W. A. Benjamin, New York, 1970); P. G. Burke, Potential Scattering in Atomic Physics (Plenum, New York, 1977); Yu. N. Demkov and G. F. Drukarev, Z. Eksp. i Teor. Fiz. 81, 1218 (1981); F. M. Toyama and Y. Nogami, Phys. Rev. C38, 2881 (1988); B. N. Zakhariev and A. A. Suzko, Direct and Inverse Problems: Potentials in Quantum Scattering (Springer-Verlag, Berlin, 1990).
    • (1988) Phys. Rev. , vol.C38 , pp. 2881
    • Toyama, F.M.1    Nogami, Y.2
  • 36
    • 0003979265 scopus 로고
    • Springer-Verlag, Berlin
    • S. Gelman, Topics in Atomic Collision Theory (Academic, New York, 1969); B. H. Bransden, Atomic Collision Theory (W. A. Benjamin, New York, 1970); P. G. Burke, Potential Scattering in Atomic Physics (Plenum, New York, 1977); Yu. N. Demkov and G. F. Drukarev, Z. Eksp. i Teor. Fiz. 81, 1218 (1981); F. M. Toyama and Y. Nogami, Phys. Rev. C38, 2881 (1988); B. N. Zakhariev and A. A. Suzko, Direct and Inverse Problems: Potentials in Quantum Scattering (Springer-Verlag, Berlin, 1990).
    • (1990) Direct and Inverse Problems: Potentials in Quantum Scattering
    • Zakhariev, B.N.1    Suzko, A.A.2
  • 37
    • 0009184608 scopus 로고
    • G. A. Natanzon, Teor. Mat. Fiz. 38, 146 (1979); L. E. Gendenshtein, JETP Lett. 38, 356 (1983); F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); J. Dabrowska, A. Khare and U. Sukhatme, J. Phys. A21, L195 (1988); 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).
    • (1979) Teor. Mat. Fiz. , vol.38 , pp. 146
    • Natanzon, G.A.1
  • 38
    • 0009184608 scopus 로고
    • G. A. Natanzon, Teor. Mat. Fiz. 38, 146 (1979); L. E. Gendenshtein, JETP Lett. 38, 356 (1983); F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); J. Dabrowska, A. Khare and U. Sukhatme, J. Phys. A21, L195 (1988); 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).
    • (1983) JETP Lett. , vol.38 , pp. 356
    • Gendenshtein, L.E.1
  • 39
    • 4244161498 scopus 로고
    • G. A. Natanzon, Teor. Mat. Fiz. 38, 146 (1979); L. E. Gendenshtein, JETP Lett. 38, 356 (1983); F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); J. Dabrowska, A. Khare and U. Sukhatme, J. Phys. A21, L195 (1988); 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).
    • (1987) Phys. Rev. , vol.D36 , pp. 2438
    • Cooper, F.1    Ginocchi, J.N.2    Khare, A.3
  • 40
    • 0001718696 scopus 로고
    • G. A. Natanzon, Teor. Mat. Fiz. 38, 146 (1979); L. E. Gendenshtein, JETP Lett. 38, 356 (1983); F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); J. Dabrowska, A. Khare and U. Sukhatme, J. Phys. A21, L195 (1988); 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).
    • (1988) J. Phys. , vol.A21
    • Dabrowska, J.1    Khare, A.2    Sukhatme, U.3
  • 41
    • 0009184608 scopus 로고
    • G. A. Natanzon, Teor. Mat. Fiz. 38, 146 (1979); L. E. Gendenshtein, JETP Lett. 38, 356 (1983); F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); J. Dabrowska, A. Khare and U. Sukhatme, J. Phys. A21, L195 (1988); 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).
    • (1988) Am. J. Phys. , vol.56 , pp. 163
    • Dutt, R.1    Khare, A.2    Sukhatme, U.P.3
  • 42
    • 0009184608 scopus 로고
    • G. A. Natanzon, Teor. Mat. Fiz. 38, 146 (1979); L. E. Gendenshtein, JETP Lett. 38, 356 (1983); F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); J. Dabrowska, A. Khare and U. Sukhatme, J. Phys. A21, L195 (1988); 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).
    • (1991) Am. J. Phys. , vol.59 , pp. 723
  • 43
    • 0001237410 scopus 로고
    • G. A. Natanzon, Teor. Mat. Fiz. 38, 146 (1979); L. E. Gendenshtein, JETP Lett. 38, 356 (1983); F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); J. Dabrowska, A. Khare and U. Sukhatme, J. Phys. A21, L195 (1988); 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).
    • (1989) J. Phys. , vol.A22 , pp. 689
    • Lévai, G.1
  • 44
    • 0009184608 scopus 로고
    • G. A. Natanzon, Teor. Mat. Fiz. 38, 146 (1979); L. E. Gendenshtein, JETP Lett. 38, 356 (1983); F. Cooper, J. N. Ginocchi and A. Khare, Phys. Rev. D36, 2438 (1987); J. Dabrowska, A. Khare and U. Sukhatme, J. Phys. A21, L195 (1988); 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).
    • (1994) J. Phys. , vol.27 , pp. 3809
  • 46
    • 36149008139 scopus 로고
    • 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-Massachusetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
    • (1935) Phys. Rev. , vol.48 , pp. 161
    • Manning, M.F.1
  • 47
    • 51249195748 scopus 로고
    • 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-Massachusetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
    • (1962) Nuovo Cimento , vol.25 , pp. 864
    • Bhattacharjie, A.1    Sudarshan, E.C.G.2
  • 48
    • 0001193423 scopus 로고
    • 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-Massachusetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
    • (1984) Phys. Lett. , vol.A103 , pp. 298
    • Pak, N.K.1    Sökmen, I.2
  • 49
    • 36149008139 scopus 로고
    • Addison-Wesley, ReadingMassachusetts
    • 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-Massachusetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
    • (1986) Classical Mechanics
    • Goldstein, H.G.1
  • 50
    • 0000224354 scopus 로고
    • 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-Massachusetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
    • (1987) Phys. Rev. , vol.A36 , pp. 1562
    • Montemayer, R.1
  • 51
    • 0039242144 scopus 로고
    • 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-Massachusetts, 1986); R. Montemayer, Phys. Rev. A36, 1562 (1987); G. Junker, J. Phys. A23, L881 (1990).
    • (1990) J. Phys. , vol.A23
    • Junker, G.1
  • 53
    • 0000984539 scopus 로고
    • 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).
    • (1989) J. Phys. , vol.A22
    • Moshinsky, M.1    Szczepaniak, A.2
  • 54
    • 3342879807 scopus 로고
    • 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).
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 1643
    • Bentez, J.1    Martinez-y-Romero, R.P.2    Nunez-Yepez, H.N.3    Salas-Brito, A.L.4
  • 55
    • 0039546838 scopus 로고
    • 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).
    • (1991) J. Phys. , vol.A24 , pp. 667
    • De Lange, O.L.1
  • 56
    • 0001645583 scopus 로고
    • 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).
    • (1994) Phys. Rev. , vol.A49 , pp. 586
    • Villalba, V.M.1
  • 57
    • 0039520059 scopus 로고    scopus 로고
    • 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).
    • (1999) J. Phys. , vol.A32 , pp. 5367
    • Rozmej, P.1    Arvieu, R.2
  • 59
    • 0037030031 scopus 로고    scopus 로고
    • A. D. Alhaidari, Phys. Rev. Lett. 87, 210405 (2001); 88, 189901 (2002).
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 189901
  • 60
    • 0035941172 scopus 로고    scopus 로고
    • A. D. Alhaidari, J. Phys. A34, 9827 (2001); 35, 6207 (2002).
    • (2001) J. Phys. , vol.A34 , pp. 9827
    • Alhaidari, A.D.1
  • 61
    • 0035941172 scopus 로고    scopus 로고
    • A. D. Alhaidari, J. Phys. A34, 9827 (2001); 35, 6207 (2002).
    • (2002) J. Phys. , vol.35 , pp. 6207
  • 62
    • 0004059388 scopus 로고
    • Academic, New York
    • W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Giirsey and F. Iaehello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N. Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iaehello 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).
    • (1968) Lie Theory and Special Functions
    • Miller W., Jr.1
  • 63
    • 0001609401 scopus 로고
    • W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Giirsey and F. Iaehello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N. Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iaehello 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).
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 873
    • Alhassid, Y.1    Giirsey, F.2    Iaehello, F.3
  • 64
    • 0007376875 scopus 로고
    • W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Giirsey and F. Iaehello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N. Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iaehello 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).
    • (1983) Ann. Phys. (N. Y.) , vol.148 , pp. 346
  • 65
    • 0007434577 scopus 로고
    • W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Giirsey and F. Iaehello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N. Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iaehello 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).
    • (1986) Ann. Phys. (N. Y.) , vol.167 , pp. 181
  • 66
    • 4243712303 scopus 로고
    • W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Giirsey and F. Iaehello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N. Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iaehello 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).
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 271
    • Alhassid, Y.1    Iaehello, F.2    Wu, J.3
  • 67
    • 11744269813 scopus 로고
    • W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Giirsey and F. Iaehello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N. Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iaehello 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).
    • (1990) J. Math. Phys. , vol.31 , pp. 557
    • Wu, J.1    Alhassid, Y.2
  • 68
    • 36149030230 scopus 로고
    • W. Miller Jr., Lie Theory and Special Functions (Academic, New York, 1968); Y. Alhassid, F. Giirsey and F. Iaehello, Phys. Rev. Lett. 50, 873 (1983); Ann. Phys. (N. Y.) 148, 346 (1983); ibid. 167, 181 (1986); Y. Alhassid, F. Iaehello 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).
    • (1991) J. Phys. , vol.A24 , pp. 3557
    • Englefield, M.J.1    Quesne, C.2
  • 71
    • 0003930334 scopus 로고
    • Springer-Verlag, Berlin
    • A. Bohm, Quantum Mechanics (Springer-Verlag, Berlin, 1979); O. Castanos, A. Frank and R. Lopez Pena, Proc. XIV Symp. on Nuclear Physics, ed. M.-E. Brandan (World Scientific, Singapore, 1991), p. 233.
    • (1979) Quantum Mechanics
    • Bohm, A.1
  • 72
  • 74
    • 0010118680 scopus 로고
    • M. Flato and C. Fronsdal, Lett. Math. Phys. 2, 421 (1978); Phys. Lett. B97, 236 (1980).
    • (1980) Phys. Lett. , vol.B97 , pp. 236


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