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Coherent states for the supersymmetric partners of the truncated oscillator

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Abstract.

We build the coherent states for a family of solvable singular Schrödinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their eigenfunctions are not completely connected by their natural ladder operators. We find a definition that behaves appropriately in the complete Hilbert space of the system, through linearised ladder operators. In doing so, we study basic properties of such states like continuity in the complex parameter, resolution of the identity, probability density, time evolution and possibility of entanglement.

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References

  1. E. Schrödinger, Naturwissenschaften 14, 664 (1926)

    Article  ADS  Google Scholar 

  2. J.R. Klauder, J. Math. Phys. 4, 1955 (1963)

    Google Scholar 

  3. J.R. Klauder, J. Math. Phys. 4, 1958 (1963)

    Google Scholar 

  4. R.J. Glauber, Phys. Rev. 130, 2529 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  5. R.J. Glauber, Phys. Rev. 131, 2766 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  6. A. Perelomov, Generalized Coherent States and their Applications (Springer, 1986)

  7. J.P. Gazeau J.R. Klauder, J. Phys. A: Math. Gen. 32, 123 (1999)

    Article  ADS  Google Scholar 

  8. S.T. Ali, J.P. Antoine J.P. Gazeau, Coherent States, Wavelets and their Generalizations, 2nd edition (Springer, 2014)

  9. C. Quesne, Ann. Phys. 293, 147 (2001)

    Article  ADS  Google Scholar 

  10. M. Angelova, V. Hussin, J. Phys. A 41, 30416 (2008)

    Article  Google Scholar 

  11. E. Witten, Nucl. Phys. B 185, 513 (1981)

    Article  ADS  Google Scholar 

  12. E. Witten, Nucl. Phys. B 202, 253 (1982)

    Article  ADS  Google Scholar 

  13. B. Mielnik, J. Math. Phys. 25, 3387 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  14. A.A. Andrianov, M.V. Ioffe, V.P. Spiridonov, Phys. Lett. A 174, 273 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  15. A.A. Andrianov, M.V. Ioffe, F. Cannata, J.P. Dedonder, Int. J. Mod. Phys. A 10, 2683 (1995)

    Article  ADS  Google Scholar 

  16. F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  17. V.G. Bagrov, B.F. Samsonov, Phys. Part. Nucl. 28, 374 (1997)

    Article  Google Scholar 

  18. D.J. Fernández, M.L. Glasser, L.M. Nieto, Phys. Lett. A 240, 15 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  19. D.J. Fernández, V. Hussin, B. Mielnik, Phys. Lett. A 244, 309 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  20. G. Junker, P. Roy, Ann. Phys. 270, 155 (1998)

    Article  ADS  Google Scholar 

  21. C. Quesne, N. Vansteenkiste, Helv. Phys. Acta 72, 71 (1999)

    MathSciNet  Google Scholar 

  22. B.F. Samsonov, Phys. Lett. A 263, 274 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  23. B. Mielnik, L.M. Nieto, O. Rosas-Ortiz, Phys. Lett. A 269, 70 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  24. J.F Cariñena, A. Ramos, D.J. Fernández, Ann. Phys. 292, 42 (2001)

    Article  ADS  Google Scholar 

  25. H. Aoyama, M. Sato, T. Tanaka, Nucl. Phys. B 619, 105 (2001)

    Article  ADS  Google Scholar 

  26. B. Mielnik, O. Rosas-Ortiz, J. Phys. A: Math. Gen. 37, 10007 (2004)

    Article  ADS  Google Scholar 

  27. J.M. Carballo, D.J. Fernández, J. Negro, L.M. Nieto, J. Phys. A: Math. Gen. 37, 10349 (2004)

    Article  ADS  Google Scholar 

  28. D.J. Fernández, N. Fernández-García, AIP Conf. Proc. 744, 236 (2005)

    Article  MathSciNet  Google Scholar 

  29. A. Contreras-Astorga, D.J. Fernández, J. Phys. A: Math. Theor. 41, 475303 (2008)

    Article  Google Scholar 

  30. I. Marquette, J. Math. Phys. 50, 095202 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  31. D.J. Fernández, AIP Conf. Proc. 1287, 3 (2010)

    Google Scholar 

  32. C. Quesne, Mod. Phys. Lett. A 26, 1843 (2011)

    Article  ADS  Google Scholar 

  33. D. Bermúdez, D.J. Fernández, SIGMA 7, 025 (2011)

    Google Scholar 

  34. I. Marquette, J. Math. Phys. 53, 012901 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  35. A.A. Andrianov, M.V. Ioffe, J. Phys. A: Math. Theor. 45, 503001 (2012)

    Article  Google Scholar 

  36. D. Gómez-Ullate, Y. Grandati, R. Milson, J. Phys. A: Math. Theor. 47, 015203 (2014)

    Article  ADS  Google Scholar 

  37. V.V. Dodonov, I.A. Malkin, V.I. Man’ko, Physica 72, 597 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  38. C.C. Gerry, J. Mod. Opt. 40, 1053 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  39. V.V. Dodonov, Ya.A. Korennoy, V.I. Man’ko, Y.A. Moukhin, Quantum Semiclass. Opt. 8, 413 (1996)

    Article  ADS  Google Scholar 

  40. I.F. Márquez, J. Negro, L.M. Nieto, J. Phys. A: Math. Gen. 31, 4115 (1998)

    Article  ADS  Google Scholar 

  41. D.J. Fernández, M. Gadella, L.M. Nieto, SIGMA 7, 029 (2011)

    Google Scholar 

  42. D.J. Fernández, V.S. Morales-Salgado, J. Phys. A: Math. Theor. 47, 035304 (2014)

    Article  ADS  Google Scholar 

  43. D.J. Fernández, V.S. Morales-Salgado, J. Phys. A: Math. Theor. 49, 195202 (2016)

    Article  ADS  Google Scholar 

  44. D.J. Fernández, V.S. Morales-Salgado, Ann. Phys. 388, 122 (2018)

    Article  ADS  Google Scholar 

  45. H.A. Buchdahl, Am. J. Phys. 35, 210 (1967)

    Article  ADS  Google Scholar 

  46. B. Bagchi, P.K. Roy, Phys. Lett. A 200, 411 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  47. D.J. Fernández, V. Hussin, O. Rosas-Ortiz, J. Phys. A: Math. Theor. 40, 6491 (2007)

    Article  ADS  Google Scholar 

  48. D. Bermudez, A. Contreras-Astorga, D.J. Fernández, Ann. Phys. 350, 615 (2014)

    Article  ADS  Google Scholar 

  49. D. Bermudez, D.J. Fernández, J. Negro, J. Phys. A: Math. Theor. 49, 335203 (2016)

    Article  Google Scholar 

  50. H. Weyl, Math. Ann. 68, 220 (1910)

    Article  MathSciNet  Google Scholar 

  51. J. von Neumann, Math. Ann. 102, 49 (1929)

    Article  Google Scholar 

  52. D.F. Walls, Nature 306, 141 (1983)

    Article  ADS  Google Scholar 

  53. R. Loudon, P.L. Knight, J. Mod. Opt. 34, 709 (1987)

    Article  ADS  Google Scholar 

  54. H. Fearn, R. Loudon, Opt. Commun. 64, 485 (1987)

    Article  ADS  Google Scholar 

  55. S.M. Tan, D.F. Walls, M.J. Collett, Phys. Rev. Lett. 66, 252 (1991)

    Article  ADS  Google Scholar 

  56. S. Scheel, D.G. Welsch, Phys. Rev. A 64, 063811 (2001)

    Article  ADS  Google Scholar 

  57. M.S. Kim, A. Son, V. Buek, P.L. Knight, Phys. Rev. A 65, 032323 (2002)

    Article  ADS  Google Scholar 

  58. W. Xiang-Bin, Phys. Rev. A 66, 024303 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  59. C. Gerry, P. Knight Introductory Quantum Optics (Cambridge University Press, 2005)

  60. D.R. Truax, Phys. Rev. D 31, 1988 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  61. A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev, Integrals and Series, Vol. 2: Special Functions (Gordon and Breach, 1990)

  62. A. Shabat, Inverse Probl. 8, 303 (1992)

    Article  ADS  Google Scholar 

  63. A.P. Veselov, A.B. Shabat, Funct. Anal. Appl. 27, 81 (1993)

    Article  MathSciNet  Google Scholar 

  64. V.E. Adler, Physica D 73, 335 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  65. S.Y. Dubov, V.M. Eleonskii, N.E. Kulagin, Chaos 4, 47 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  66. V.M. Eleonskii, V.G. Korolev, N.E. Kulagin, Chaos 4, 583 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  67. U.P. Sukhatme, C. Rasinariu, A. Khare, Phys. Lett. A 234, 401 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  68. A.A. Andrianov, F. Cannata, M. Ioffe, D. Nishnianidze, Phys. Lett. A 266, 341 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  69. J. Mateo, J. Negro, J. Phys. A: Math. Theor. 41, 045204 (2008)

    Article  ADS  Google Scholar 

  70. K. Zelaya, O. Rosas-Ortiz, Z. Blanco, S. Cruz y Cruz, Adv. Math. Phys. 2017, 7168592 (2017)

    Article  Google Scholar 

  71. B. Mojaveri, A. Dehghani, Jafarzadeh Bahrbeig, Eur. Phys. J. Plus 133, 346 (2018)

    Article  Google Scholar 

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Correspondence to Vicente Said Morales-Salgado.

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Fernández C., D.J., Hussin, V. & Morales-Salgado, V.S. Coherent states for the supersymmetric partners of the truncated oscillator. Eur. Phys. J. Plus 134, 18 (2019). https://doi.org/10.1140/epjp/i2019-12394-7

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