Advertisement

International Journal of Theoretical Physics

, Volume 50, Issue 7, pp 1993–2001 | Cite as

Rosen–Morse Potential and Its Supersymmetric Partners

  • Samuel Domínguez-Hernández
  • David J. Fernández C.
Article

Abstract

A set of supersymmetric partners of the Rosen–Morse potential is generated. The corresponding physical properties are studied—in particular, the change in intensity of the singularities at the boundaries of the domain.

Keywords

Supersymmetric quantum mechanics Rosen–Morse potentials Shape invariance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Miller, W.: Lie Theory and Special Functions. Academic Press, New York (1968) MATHGoogle Scholar
  2. 2.
    de Lange, O.L., Raab, R.E.: Operator Methods in Quantum Mechanics. Clarendon, Oxford (1991) Google Scholar
  3. 3.
    Cooper, F., Khare, A., Sukhatme, U.: Supersymmetry and quantum mechanics. Phys. Rep. 251, 267–385 (1995) MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Mielnik, B., Rosas-Ortiz, O.: Factorization: little or great algorithm? J. Phys. A 37, 10007–10035 (2004) MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Fernández, D.J., Fernández-García, N.: Higher-order supersymmetric quantum mechanics. AIP Conf. Proc. 744, 236–273 (2005) CrossRefGoogle Scholar
  6. 6.
    Fernández, D.J.: Supersymmetric quantum mechanics. arXiv:0910.0192v1 [quant-ph] (2009)
  7. 7.
    Andrianov, A.A., Borisov, N.V., Ioffe, M.V.: Factorization method and Darboux transformation for multidimensional Hamiltonians. Theor. Math. Phys. 61, 1078–1088 (1984) CrossRefGoogle Scholar
  8. 8.
    Bagrov, V.G., Samsonov, B.F.: Darboux transformation of the Schrödinger equation. Phys. Part. Nucl. 28, 374–397 (1997) MathSciNetCrossRefGoogle Scholar
  9. 9.
    Fernández, D.J., Rosu, H.C.: Quantum mechanical spectral engineering by scaling intertwining. Phys. Scr. 64, 177–183 (2001) ADSMATHCrossRefGoogle Scholar
  10. 10.
    Andrianov, A.A., Cannata, F.: Nonlinear supersymmetry for spectral design in quantum mechanics. J. Phys. A 37, 10297–10321 (2004) MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    Fernández, D.J., Glasser, M.L., Nieto, L.M.: New isospectral oscillator potentials. Phys. Lett. A 240, 15–20 (1998) MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    Fernández, D.J., Hussin, V., Mielnik, B.: A simple generation of exactly solvable anharmonic oscillators. Phys. Lett. A 244, 309–316 (1998) MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Fernández, D.J., Hussin, V.: Higher order SUSY, linearized non-linear Heisenberg algebras and coherent states. J. Phys. A 32, 3603–3619 (1999) MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    Díaz, J.I., Negro, J., Nieto, L.M., Rosas-Ortiz, O.: The supersymmetric modified Pöschl–Teller and delta-well potentials. J. Phys. A 32, 8447–8460 (1999) MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    Negro, J., Nieto, L.M., Rosas-Ortiz, O.: Confluent hypergeometric equations and related solvable potentials in quantum mechanics. J. Math. Phys. 41, 7964–7996 (2000) MathSciNetADSMATHCrossRefGoogle Scholar
  16. 16.
    Fernández, D.J., Hussin, V., Rosas-Ortiz, O.: Coherent states for Hamiltonians generated by supersymmetry. J. Phys. A 40, 6491–6511 (2007) MathSciNetADSMATHCrossRefGoogle Scholar
  17. 17.
    Contreras-Astorga, A., Fernández, D.J.: Supersymmetric partners of the trigonometric Pöschl–Teller potentials. J. Phys. A 41, 475303 (2008) MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    Compean, C.B., Kirchbach, M.: The trigonometric Rosen–Morse potential in the supersymmetric quantum mechanics and its exact solutions. J. Phys. A 39, 547–557 (2006) MathSciNetADSMATHCrossRefGoogle Scholar
  19. 19.
    Nieto, L.M., Santander, M., Rosu, H.C.: Hydrogen atom as an eigenvalue problem in 3-D spaces of constant curvature and minimal length. Mod. Phys. Lett. A 14, 2463–2469 (1999) ADSCrossRefGoogle Scholar
  20. 20.
    Andrianov, A.A., Ioffe, M.V., Spiridonov, V.: Higher-derivative supersymmetry and the Witten index. Phys. Lett. A 174, 273–279 (1993) MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    Andrianov, A.A., Ioffe, M.V., Cannata, F., Dedonder, J.P.: 2nd-order derivative supersymmetry, q-deformations and the scattering problem. Int. J. Mod. Phys. A 10, 2683–2702 (1995) MathSciNetADSMATHCrossRefGoogle Scholar
  22. 22.
    Fernández, D.J.: SUSUSY quantum mechanics. Int. J. Mod. Phys. A 12, 171–176 (1997) ADSMATHCrossRefGoogle Scholar
  23. 23.
    Samsonov, B.F.: New possibilities for supersymmetry breakdown in quantum mechanics and second-order irreducible Darboux transformations. Phys. Lett. A 263, 274–280 (1999) MathSciNetADSMATHCrossRefGoogle Scholar
  24. 24.
    Plyushchay, M.: Hidden nonlinear supersymmetries in pure parabosonic systems. Int. J. Mod. Phys. A 15, 3679–3698 (2000) MathSciNetADSMATHGoogle Scholar
  25. 25.
    Aoyama, H., Sato, M., Tanaka, T.: N-fold supersymmetry in quantum mechanics: general formalism. Nucl. Phys. B 619, 105–127 (2001) MathSciNetADSMATHCrossRefGoogle Scholar
  26. 26.
    Plyushchay, M.: Nonlinear supersymmetry: from classical to quantum mechanics. J. Phys. A 37, 10375–10384 (2004) MathSciNetADSMATHCrossRefGoogle Scholar
  27. 27.
    Compean, C.B., Kirchbach, M.: Trigonometric quark confinement potential of QCD traits. Eur. Phys. J. A 33, 1–4 (2007) ADSCrossRefGoogle Scholar
  28. 28.
    Bateman, H.: Higher Transcendental Functions, vol. 1. McGraw-Hill, New York (1953) Google Scholar
  29. 29.
    Chenaghlou, A., Faizy, O.: Gazeau–Klauder coherent states for trigonometric Rosen–Morse potential. J. Math. Phys. 49, 022104 (2008) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Samuel Domínguez-Hernández
    • 1
  • David J. Fernández C.
    • 2
  1. 1.Ciencias BásicasUPIITA-IPNMéxicoMexico
  2. 2.Departamento de FísicaCinvestavMéxicoMexico

Personalised recommendations