Quantization and Stable Attractors in a DissipativeOrbital Motion
Daniel L. Nascimento, Antonio L. A. Fonseca
.
DOI: 10.4236/jmp.2011.24030   PDF    HTML     7,269 Downloads   11,293 Views   Citations

Abstract

We present a method for determining the motion of an electron in a hydrogen atom, which starts from a field Lagrangean foundation for non-conservative systems that can exhibit chaotic behavior. As a consequence, the problem of the formation of the atom becomes the problem of finding the possible stable orbital attractors and the associated transition paths through which the electron mechanical energy varies continuously until a stable energy state is reached.

Share and Cite:

D. Nascimento and A. Fonseca, "Quantization and Stable Attractors in a DissipativeOrbital Motion," Journal of Modern Physics, Vol. 2 No. 4, 2011, pp. 219-224. doi: 10.4236/jmp.2011.24030.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] E. Schr?dinger, “Quantisierung als Eigenwertproblem,” Annalen der Physik, Vol. 79, No. 4, 1926, pp. 361-376.
[2] A. Einstein, “Zum Quantensatz von Sommerfeld und Epstein,” Physikalische Gesellschaft Verhandlungen, Vol. 19, 1917, pp. 82-92.
[3] M. C. Gutzwiller, “Phase-Integral Approximation in Momentum Space and the Bound States of an Atom,” Journal of Mathematical Physics, Vol. 8, No. 10, 1967 pp. 1979-2000. doi:10.1063/1.1705112
[4] M. C. Gutzwiller, “Phase-Integral Approximation in Momentum Space and the Bound States of an Atom II,” Journal of Mathematical Physics, Vol. 10, No. 6, 1969, pp. 1004-1020. doi:10.1063/1.1664927
[5] M. C. Gutzwiller, “Energy Spectrum According to Classical Mechanics,” Journal of Mathematical Physics, Vol. 11, No. 6, 1970, pp. 1791-806. doi:10.1063/1.1665328
[6] M. C. Gutzwiller, “Periodic Orbits and Classical Quantization Conditions,” Journal of Mathematical Physics, Vol. 12, No. 3, 1971 pp. 343 -358. doi:10.1063/1.1665596
[7] M. C. Gutzwiller, “Chaos in Classical and Quantum Physics,” Springer Verlag, Berlin, 1990.
[8] J. H. Hannay, A. M. Ozorio de Almeida, “Periodic Orbits and the Correlation Function for the Density of States,” Journal of Physics A: Mathematical and General, Vol. 17, No. 21, 1984, pp. 3429-3440. doi:10.1088/0305-4470/17/18/013
[9] A. M. Ozorio de Almeida, J. H. Hannay, “Resonant Periodic Orbits and the Semiclassical Energy Spectrum,” Journal of Physics A: Mathematical and General, Vol. 20, No. 17, 1987, pp. 5873-5883. doi:10.1088/0305-4470/20/17/021
[10] A. M. Ozorio de Almeida, “The Weyl Representation in Classical and Quantum Mechanics,” Physics Reports, Vol. 215, 1998, pp. 265-344. doi:10.1016/S0370-1573(97)00070-7
[11] A. M. Ozorio de Almeida, “Hamiltonian Systems: Chaos and Quantization,” Cambridge University Press, Cambridge, 1989.
[12] D. L. Nascimento, A. L. A. Fonseca, “A new Approach Using the Relativistic Hamilton-Jacobi Equation to Evaluate the Correct Energy Levels of the Hydrogen Atom,” International Journal of Quantum Chemistry, Vol. 106, No. 2006, pp. 2779-2789.
[13] A. L. A. Fonseca, D. L. Nascimento, “New Approach to Researches in Relativistic Quantum Chemistry Using Hamilton-Jacobi Equation,” In: Quantum Chemistry Research Trends, Nova Science Publishers, New York, 2007, pp. 173-204.
[14] D. L. Nascimento, A. L. A. Fonseca, “2D Spinless Version of Dirac’s Equation Written in a Noninertial Frame of Reference,” International Journal of Quantum Chemistry, 2010: in press.
[15] H. Goldstein, “Classical Mechanics,” Addison-Wesley Reading, Boston, 1950.
[16] L. I. Schiff, “Quantum Mechanics,” McGraw-Hill, New York, 1968.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.