Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results
2004 | 105 | 3 | 253-262

Article title

Invariants for Time-Dependent Harmonic Oscillators from the Real Representation of Solution

Authors

Content

Title variants

Languages of publication

EN

Abstracts

EN
The invariants for the time-dependent one-dimensional harmonic oscillator and the time-dependent two-dimensional harmonic oscillator in a static magnetic field are derived from the real representation of the exact solution to the equation of motion. Mathematically, the orthogonal functions invariant is the angular momentum of an isotropic time-dependent two-dimensional harmonic oscillator. Based on the invariants obtained here, the wave function for time-dependent two-dimensional harmonic oscillator in a static magnetic field in cylindrical coordinate is simply derived and the dynamical and geometrical phases are easily got by expressing the wave function as the superpositions of the wave functions of time-dependent two-dimensional harmonic oscillator in rectangular coordinate. For the driven system, the driving induced dynamical phase and the geometrical phase are respectively associated with the classical Hamiltonian and de Broglie wave of the center motion of the wave function.

Keywords

EN

Contributors

author
  • Department of Applied Physics, School of Science, Tianjin University, Tianjin 300072, China
  • LiuHui Center for Applied Mathematics, Tianjin 300071, China
author
  • Department of Applied Physics, School of Science, Tianjin University, Tianjin 300072, China
author
  • Department of Applied Physics, School of Science, Tianjin University, Tianjin 300072, China

References

  • 1. H.R. Lewis, Phys. Rev. Lett. 18, 510 (1967); H.R. Lewis, W.B. Riesenfeld, J. Math. Phys. 10, 1458 (1969)
  • 2. P.G.L. Leach, SIAM J. Appl. Math. 34, 496 (1978)
  • 3. M. Lutzky, Phys. Lett. A 68, 3 (1978)
  • 4. M.F. Guasti, A. Gil-Villegas, Phys. Lett. A 292, 243 (2002)
  • 5. I.A. Pedrosa, Phys. Rev. A 55, 3219 (1997)
  • 6. C.A.S. Ferreira, P.T.S. Alencar, J.M.F. Bassalo, Phys. Rev. A 66, 024103 (2002)
  • 7. Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987)
  • 8. S.S. Mizrahi, Phys. Lett. A 138, 465 (1989)
  • 9. K. Husimi, Prog. Theor. Phys. 9, 381 (1953)
  • 10. M.L. Liang, H.B. Wu, Phys. Scr. 68, 41 (2003)
  • 11. See for example Y.F. Liu, Y.A. Lei, J.Y. Zeng, Phys. Lett. A 231, 9 (1997)

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.bwnjournal-article-appv105n304kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.