Effective Hamiltonian with position-dependent mass and ordering problem

  • V. M. TkachukEmail author
  • O. Voznyak
Regular Article


We derive the effective low-energy Hamiltonian for the tight-binding model with the hopping integral slowly varying along the chain. The effective Hamiltonian contains the kinetic energy with position-dependent mass, which is inverse to the hopping integral, and effective potential energy. Changing of ordering in the kinetic energy leads to change of the effective potential energy and leaves the Hamiltonian the same one. Therefore, we can choose arbitrary von Roos ordering parameters in the kinetic energy without changing the Hamiltonian. Moreover, we propose a more general form for the kinetic energy than that of von Roos, which nevertheless together with the effective potential energy represent the same Hamiltonian.


Kinetic Energy Potential Energy Hermitian Form Schrodinger Equation Dependent Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    M.R. Geller, W. Kohn, Phys. Rev. Lett. 70, 3103 (1993).ADSCrossRefGoogle Scholar
  2. 2.
    Ll. Serra, E. Lipparini, Europhys. Lett. 40, 667 (1997).ADSCrossRefGoogle Scholar
  3. 3.
    A. Puente, L. I. Serra, M. Casas, Z. Phys. D 31, 283 (1994).ADSCrossRefGoogle Scholar
  4. 4.
    C. Quesne, J. Phys. A: Math. Theor. 40, 13107 (2007).MathSciNetADSCrossRefzbMATHGoogle Scholar
  5. 5.
    O. von Roos, Phys. Rev. B 27, 7547 (1983).ADSCrossRefGoogle Scholar
  6. 6.
    G.T. Einevoll, P.C. Hemmer, J. Thomsen, Phys. Rev. B 42, 3485 (1990).ADSCrossRefGoogle Scholar
  7. 7.
    G.T. Einevoll, Phys. Rev. B 42, 3497 (1990).ADSCrossRefGoogle Scholar
  8. 8.
    A. de Souza Dutra, C.A.S. Almeida, Phys. Lett. A 275, 25 (2000).MathSciNetADSCrossRefzbMATHGoogle Scholar
  9. 9.
    C. Quesne, V.M. Tkachuk, J. Phys. A 37, 4267 (2004).MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    B. Bagchi, A. Banerjee, C. Quesne, V.M. Tkachuk, J. Phys. A 38, 2929 (2005).MathSciNetADSCrossRefzbMATHGoogle Scholar
  11. 11.
    S. Habib Mazharimousavi, O. Mustafa, Phys. Scr. 87, 055008 (2013).ADSCrossRefGoogle Scholar
  12. 12.
    O. Mustafa, S. Habib Mazharimousavi, Int. J. Theor. Phys. 46, 1786 (2007).CrossRefzbMATHGoogle Scholar
  13. 13.
    K. Young, Phys. Rev. B 39, 13434 (1989).ADSCrossRefGoogle Scholar
  14. 14.
    M. Vubangsi, M.Tchoffo, L.C. Fai, Eur. Phys. J. Plus 129, 105 (2014).CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department for Theoretical PhysicsIvan Franko National University of LvivLvivUkraine

Personalised recommendations