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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 358198, 9 pages
http://dx.doi.org/10.1155/2011/358198
Research Article

Quasi-Exact Solvability of a Hyperbolic Intermolecular Potential Induced by an Effective Mass Step

Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN 46408, USA

Received 3 December 2010; Accepted 11 January 2011

Academic Editor: N. Govil

Copyright © 2011 Axel Schulze-Halberg. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. Grosche, “Path integral solutions for deformed Pöschl-Teller-like and conditionally solvable potentials,” Journal of Physics A, vol. 38, no. 13, pp. 2947–2958, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. H. Eğrifes, D. Demirhan, and F. Büyükkılıç, “Exact solutions of the Schrödinger equation for the deformed hyperbolic potential well and the deformed four-parameter exponential type potential,” Physics Letters A, vol. 275, no. 4, pp. 229–237, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. H. Eğrifes, D. Demirhan, and F. Büyükkılıç, “Exact solutions of the Schrödinger equation for two deformed hyperbolic molecular potentials,” Physica Scripta, vol. 60, no. 3, pp. 195–198, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. T. Gora and F. Williams, “Electronic states of homogeneous and inhomogeneous mixed semiconductors,” in II-VI Semiconducting Compounds, D. G. Thomas, Ed., Benjamin, New York, NY, USA, 1967. View at Google Scholar
  5. T. Gora and F. Williams, “Theory of electronic states and transport in graded mixed semiconductors,” Physical Review, vol. 177, no. 3, pp. 1179–1182, 1969. View at Publisher · View at Google Scholar
  6. G. T. Landsberg, Solid State Theory: Methods and Applications, Wiley-Interscience, London, UK, 1969.
  7. A. D. Alhaidari, “Solutions of the nonrelativistic wave equation with position-dependent effective mass,” Physical Review A, vol. 66, no. 4, Article ID 042116, 7 pages, 2002. View at Google Scholar
  8. B. Bagchi, P. S. Gorain, and C. Quesne, “Morse potential and its relationship with the Coulomb in a position-dependent mass background,” Modern Physics Letters A, vol. 21, no. 36, pp. 2703–2708, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. B. Bagchi, P. Gorain, C. Quesne, and R. Roychoudhury, “Effective-mass Schrödinger equation and generation of solvable potentials,” Czechoslovak Journal of Physics, vol. 54, no. 10, pp. 1019–1025, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  10. A. Ganguly and L. M. Nieto, “Shape-invariant quantum Hamiltonian with position-dependent effective mass through second-order supersymmetry,” Journal of Physics A, vol. 40, no. 26, pp. 7265–7281, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. Tanaka, “𝒩-fold supersymmetry in quantum systems with position-dependent mass,” Journal of Physics A, vol. 39, no. 1, pp. 219–234, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. Dekar, L. Chetouani, and T. F. Hammann, “An exactly soluble Schrödinger equation with smooth position-dependent mass,” Journal of Mathematical Physics, vol. 39, no. 5, pp. 2551–2563, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. L. Dekar, L. Chetouani, and T. F. Hammann, “Wave function for smooth potential and mass step,” Physical Review A, vol. 59, no. 1, pp. 107–112, 1999. View at Google Scholar
  14. K. C. Yung and J. H. Yee, “Derivation of the modified Schrödinger equation for a particle with a spatially varying mass through path integrals,” Physical Review A, vol. 50, no. 1, pp. 104–106, 1994. View at Publisher · View at Google Scholar
  15. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, Boston, Mass, USA, 1994.