About this Journal Submit a Manuscript Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 973968, 7 pages
http://dx.doi.org/10.5402/2012/973968
Research Article

Green's Second Identity for Vector Fields

Laboratorio de Óptica Cuántica, Departamento de Física, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México, DF, Mexico

Received 2 May 2012; Accepted 20 June 2012

Academic Editors: U. Kulshreshtha, P. Roy, and D. Singleton

Copyright © 2012 M. Fernández-Guasti. 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. M. Fernández Guasti, “Complementary fields conservation equation derived from the scalar wave equation,” Journal of Physics A, vol. 37, no. 13, pp. 4107–4121, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. R. K. Colegrave and M. A. Mannan, “Invariants for the time-dependent harmonic oscillator,” Journal of Mathematical Physics, vol. 29, no. 7, pp. 1580–1587, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. M. Fernández Guasti and A. Gil-Villegas, “Orthogonal functions invariant for the time-dependent harmonic oscillator,” Physics Letters A, vol. 292, no. 4-5, pp. 243–245, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. M. Fernández Guasti and H. Moya-Cessa, “Amplitude and phase representation of quantum invariants for the time dependent harmonic oscillator,” Physical Review A, vol. 67, Article ID 063803, pp. 1–5, 2003.
  5. I. A. Pedrosa and I. Guedes, “Quantum states of a generalized time-dependent inverted harmonic oscillator,” International Journal of Modern Physics B, vol. 18, no. 9, pp. 1379–1385, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. H. R. Lewis, “Classical and quantum systems with time-dependent harmonic-oscillator-type hamiltonians,” Physical Review Letters, vol. 18, no. 13, pp. 510–512, 1967. View at Publisher · View at Google Scholar · View at Scopus
  7. A. E. H. Love, “The integration of the equations of propagation of electric waves,” Philosophical Transactions of the Royal Society of London A, vol. 197, pp. 1–45, 1901.
  8. J. A. Stratton and L. J. Chu, “Diffraction theory of electromagnetic waves,” Physical Review, vol. 56, no. 1, pp. 99–107, 1939. View at Publisher · View at Google Scholar · View at Scopus
  9. N. C. Bruce, “Double scatter vector-wave Kirchhoff scattering from perfectly conducting surfaces with infinite slopes,” Journal of Optics, vol. 12, no. 8, Article ID 085701, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. W. Franz, “On the theory of diffraction,” Proceedings of the Physical Society A, vol. 63, no. 9, p. 925, 1950.
  11. C.-T. Tai, “Kirchhoff theory: scalar, vector, or dyadic?” IEEE Transactions on Antennas and Propagation, vol. 20, no. 1, pp. 114–115, 1972.
  12. G. Arfken, Mathematical Methods for Physicists, Academic Press, New York, NY, USA, 1966.