Abstract
In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence postulate of quantum mechanics. Then, without appealing to the wave function properties, we reproduce the well-known dispersion relations which predict the band structure for the energy spectrum in the Krönig-Penney model.
Similar content being viewed by others
References
Bloch, F. (1928). Z. Physik 52, 555.
Bohm, D. (1952a). Physical Review 85, 166.
Bohm, D. (1952b). Physical Review 85, 180.
Bouda, A. (2001). Foundations of Physics Letters 14, 17.
Bouda, A. and Djama, T. (2001). Physical Letters A 285, 27.
Bouda, A. and Djama, T. (2002). Physica Scripta 66, 97.
Doubrovine, B., Novikov, S., and Fomenko, A. (1982). Géométrie Contemporaine, Méthodes et Applications. 2e partie, Mir, Moscou.
Faraggi, A. E. and Matone, M. (1998a). Physical Letters B 445, 357.
Faraggi, A. E. and Matone, M. (1998b). Physical Letters B 437, 369.
Faraggi, A. E. and Matone, M. (1999). Physical Letters B 450, 34.
Faraggi, A. E. and Matone, M. (2000). International Journal of Modern Physics A 15, 1869.
Floquet, G.(1883). Annales Ecole Normale Supérieure 12(47).
Floyd, E. R. (1986). Physical Review D 34, 3246.
Floyd, E. R. (1996). Foundations of Physics Letters 9, 489.
Floyd, E. R. (2000). arXiv e-print, quant-ph/0009070.
Krönig, R. D. and Penney, W. G. (1931). Proceedings of the Royal Society London 130, 499.
Ngô, C. and Ngô, H. (1995). Physique Quantique, Masson, Paris.
Singh, J. (1996). Physics of Semiconductors and their Heterostructures. McGraw-Hill, Singapore.
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS: 03.65.Ca; 03.65.Ta; 71.20.-b
Rights and permissions
About this article
Cite this article
Bouda, A., Meziane, A.M. Band Theory in the Context of the Hamilton-Jacobi Formulation. Int J Theor Phys 45, 2339–2349 (2006). https://doi.org/10.1007/s10773-006-9204-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-006-9204-2