Abstract
In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrödinger equation. Then, in the case of separated variables, by requiring that the conjugate momentum be invariant under any linear transformation of the solutions of the Schrödinger equation used in the reduced action, we clearly identify the integration constants successively in one, two and three dimensions. In each of these cases, we analytically establish that the quantum Hamilton-Jacobi equation describes microstates not detected by the Schröodinger equation in the real wave function case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bertoldi, G., Faraggi, A. E., and Matone, M. (2000). Classical and Quantum Gravity 17, 3965.
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). Physics Letters A 285, 27.
Bouda, A. and Djama, T. (2002a). Physics Letters A 296, 312.
Bouda, A. and Djama, T. (2002b). Physica Scripta 66, 97.
Bouda, A. and Hammad, F. (2002). Acta Physica Slovaca 52, 101.
Bouda, A.(2003). International Journal of Modern Physics A 18, 3347.
Carroll, R. (1999). Canadian Journal of Physics 77, 319.
Faraggi, A. E. and Matone, M. (1998a). Physics Letters A 249, 280.
Faraggi, A. E. and Matone, M. (1998b). Physics Letters B 437, 369.
Faraggi, A. E. and Matone, M. (1998c). Physics Letters B 445, 357.
Faraggi, A. E. and Matone, M. (1999). Physics Letters B 450, 34.
Faraggi, A. E. and Matone, M. (2000). International Journal of Modern Physics A 15, 1869.
Floyd, E. R. (1982). Physical Review D 26, 1339.
Floyd, E. R. (1996a). Foundations of Physics Letters 9, 489.
Floyd, E. R. (1996b). Physics Letters A 214, 259.
Floyd, E. R. (2000). arXiv e-print, Quant-ph/0009070.
Floyd, E. R.(1986). Physics Review D 34, 3246.
Landau, L., and Lifchitz, E. (1967). Mécanique Quantique, Moscou, Edition Mir.
Matone, M. (2002a). Foundations of Physics Letters 15, 311.
Matone, M. (2002b). arXiv e-print, hep-th/0212260.
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS numbers:03.65.Ca; 03.65.Ta; 02.30.Jr.
Rights and permissions
About this article
Cite this article
Bouda, A., Meziane, A.M. The Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates. Int J Theor Phys 45, 1278–1295 (2006). https://doi.org/10.1007/s10773-006-9150-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-006-9150-z