Table of Contents Author Guidelines Submit a Manuscript
International Journal of Optics
Volume 2010 (2010), Article ID 275910, 6 pages
http://dx.doi.org/10.1155/2010/275910
Research Article

Quantum Damped Mechanical Oscillator

1Department of Physics, University of Uyo, Uyo, Nigeria
2Department of Physics, University of Calabar, Calabar, Nigeria

Received 16 October 2009; Revised 6 February 2010; Accepted 8 March 2010

Academic Editor: Ortunato Tito Arecchi

Copyright © 2010 Akpan N. Ikot et al. 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. P. Caldirola, “Forze non conservative nella meccanica quantistica,” Nuovo Cimento, vol. 18, no. 9, pp. 393–400, 1941. View at Publisher · View at Google Scholar
  2. E. Kanai, “On the quantization of the dissipative systems,” Progress of Theoretical Physics, vol. 3, no. 4, pp. 440–442, 1948. View at Publisher · View at Google Scholar
  3. S. P. Kim, A. E. Santana, and F. C. Khanna, “Decoherence of quantum damped oscillators,” Journal of the Korean Physical Society, vol. 43, no. 4 I, pp. 452–460, 2003. View at Google Scholar · View at Scopus
  4. A. N. Ikot, E. E. Ituen, I. E. Essien, and L. E. Akpabio, “Path integral evaluation of a time-dependent oscillator in an external field,” Turkish Journal of Physics, vol. 32, no. 6, pp. 305–313, 2008. View at Google Scholar · View at Scopus
  5. V. V. Dodonor, I. A. Malkim, and V. I. Man'ko, “Integrals of the motion, green functions, and coherent states of dynamical systems,” International Journal of Theoretical Physics, vol. 14, no. 1, pp. 37–54, 1975. View at Publisher · View at Google Scholar
  6. V. V. Dodonov, O.V. Man'ko, and V.T. Man'ko, “Time-dependent oscillator with Kronig-Penney excitation,” Physics Letters A, vol. 175, no. 1, pp. 1–4, 1993. View at Publisher · View at Google Scholar
  7. Y. S. Kim and V. I. Man'ko, “Time-dependent mode coupling and generation of two-mode squeezed states,” Physics Letters A, vol. 157, no. 4-5, pp. 226–228, 1991. View at Publisher · View at Google Scholar
  8. O. V. Man'ko and L. Yeh, “Correlated squeezed states of two coupled oscillators with delta-kicked frequencies,” Physics Letters A, vol. 189, no. 4, pp. 268–276, 1994. View at Publisher · View at Google Scholar
  9. T. Kiss, P. Adam, and J. Janszky, “Time-evolution of a harmonic oscillator: jumps between two frequencies,” Physics Letters A, vol. 192, no. 5-6, pp. 311–315, 1994. View at Publisher · View at Google Scholar · View at Scopus
  10. C. I. Um, K. H. Yeon, and W. H. Kahng, “The quantum damped driven harmonic oscillator,” Journal of Physics A, vol. 20, no. 3, p. 611, 1987. View at Publisher · View at Google Scholar
  11. K. H. Yeon, C. I. Um, and T. F. George, “Coherent states for the damped harmonic oscillator,” Physical Review A, vol. 36, no. 11, pp. 5287–5291, 1987. View at Publisher · View at Google Scholar
  12. K. H. Yeon, C. T. Um, W. H. Kahng, and T. F. George, “Propagators for driven coupled harmonic oscillators,” Physical Review A, vol. 38, no. 12, pp. 6224–6230, 1988. View at Publisher · View at Google Scholar
  13. V. V. Dodonov and V. I. Man'Ko, “Coherent states and the resonance of a quantum damped oscillator,” Physical Review A, vol. 20, no. 2, pp. 550–560, 1979. View at Publisher · View at Google Scholar · View at Scopus
  14. J. M. Cervero and J. Villarroel, “On the quantum theory of the damped harmonic oscillator,” Journal of Physics A, vol. 17, no. 15, pp. 2963–2971, 1984. View at Publisher · View at Google Scholar · View at Scopus
  15. R. K. Colegrave and M. Sebawe Abdalla, “Harmonic oscillator with exponentially decaying mass,” Journal of Physics A, vol. 14, no. 9, pp. 2269–2280, 1981. View at Publisher · View at Google Scholar · View at Scopus
  16. C.-I. Um, K.-H. Yeon, and T. F. George, “The quantum damped harmonic oscillator,” Physics Report, vol. 362, no. 2-3, pp. 63–192, 2002. View at Publisher · View at Google Scholar · View at Scopus
  17. H. R. Lewis Jr. and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” Journal of Mathematical Physics, vol. 10, no. 8, pp. 1458–1473, 1969. View at Publisher · View at Google Scholar · View at Scopus
  18. S. P. Kim and D. N. Page, “Classical and quantum action-phase variables for time-dependent oscillators,” Physical Review A, vol. 64, no. 1, pp. 121041–121048, 2001. View at Google Scholar · View at Scopus
  19. J. K. Kim and S. P. Kim, “One-parameter squeezed Gaussian states of a time-dependent harmonic oscillator and the selection rule for vacuum states,” Journal of Physics A, vol. 32, no. 14, pp. 2711–2718, 1999. View at Publisher · View at Google Scholar · View at Scopus
  20. S. P. Kim and C. H. Lee, “Nonequilibrium quantum dynamics of second order phase transitions,” Physical Review D, vol. 62, no. 12, Article ID 125020, pp. 1–28, 2000. View at Google Scholar · View at Scopus
  21. M. Huang and M. Wu, “The Caldirora-Kanai model and its equivalent theories for a damped oscillator,” Chinese Journal of Physics, vol. 36, no. 4, pp. 566–587, 1998. View at Google Scholar
  22. V. I. Man'ko and S. S. Safonov, “The damped quantum oscillator and a classical representation of quantum mechanics,” Theoretical and Mathematical Physics, vol. 112, no. 3, pp. 1172–1181, 1997. View at Google Scholar · View at Scopus
  23. H. Bateman, “On dissipative systems and related variational principles,” Physical Review Letters, vol. 38, no. 4, pp. 815–819, 1931. View at Publisher · View at Google Scholar
  24. H. Feshbach and Y. Tikochinsky, “Quantization of the damped harmonic oscillator,” Transactions of the New York Academy of Sciences, vol. 38 II, no. 1, pp. 44–53, 1977. View at Google Scholar
  25. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, vol. 1, McGraw-Hill, New York, NY, USA, 1953.
  26. E. Celleghini, M. Rasetti, and G. Vitiello, “Quantum dissipation,” Annals of Physics, vol. 215, no. 1, pp. 156–170, 1992. View at Publisher · View at Google Scholar
  27. V. E. Tarasov, “Quantization of non-Hamiltonian and dissipative systems,” Physics Letters A, vol. 288, no. 3-4, pp. 173–182, 2001. View at Publisher · View at Google Scholar
  28. V. E. Tarasov, “Classical canonical distribution for dissipative systems,” Modern Physics Letters B, vol. 17, no. 23, pp. 1219–1226, 2003. View at Publisher · View at Google Scholar
  29. R. Banerjee and P. Mukhejee, “A canonical approach to the quantization of the damped harmonic oscillator,” Journal of Physics A: Mathematical and General, vol. 35, no. 27, pp. 5591–5598, 2002. View at Publisher · View at Google Scholar