133
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Wavelet transform in the context of quantum mechanics and new orthogonal property of mother wavelets in parameter space

&
Pages 1835-1844 | Received 04 Oct 2007, Accepted 21 Nov 2007, Published online: 14 Jun 2008

References

  • Jaffard , S , Meyer , Y and Ryan , RD . 2001 . Wavelets, Tools for Science & Technology , Philadelphia, PA : Society for Industrial and Applied Mathematics . Shao, X.G.; Sun, L. Anal. Lett. 2001, 34, 267–280; Daubechies, I. IEEE Trans. IT 1990, 36, 961–1005; Mallat, S. IEEE Trans. PAMI 1989, 11, 674–693; Rioul, R.; Vetterli, M. IEEE SP Mag. 1991, October, 14–38.
  • Burrus , CS , Gopinath , RA and Guo , HT . 1998 . Introduction to Wavelets and Wavelet Transformation (A Primer) , Englewood Cliffs, NJ : Prentice-Hall .
  • Chiu , CK . 1992 . Introduction to Wavelets , New York : Academic .
  • Daubechies , I . 1992 . Ten Lectures on Wavelets, CBMS-NSF Series in Applied Mathematics , Society for Industrial and Applied Mathematics SIAM .
  • Pinsky , MA . 2002 . Introduction to Fourier Analysis and Wavelets , New York : Book/Cole .
  • Goodman , JW . 1968 . Introduction to Fourier Optics , New York : McGraw-Hill . Fan, H.-Y.; Klauder, J.R. Phys. Rev. A 1994, 49, 704; Onural, L. Opt. Lett. 1993, 18, 846–848; Yu, F.T.S.; Lu, G. Appl. Opt. 1994, 33, 5262–5270.
  • Fan , HY and Lu , HL . 2006 . Opt. Lett. , 31 : 3432 – 3434 . Fan, H.Y.; Lu, S.G. Opt. Lett. 2007, 32, 1507–1509.
  • Fan , HY and Lu , HL . 2006 . Opt. Lett. , 31 : 407 – 409 . ibid. 2007, 32, 554–556.
  • Castaneda , R and Garcia-Sucerquia , J . 2003 . J. Mod. Opt. , 50 : 1259 – 1275 .
  • Loudon , R and Knight , PL . 1987 . J. Mod. Opt. , 34 : 709 – 759 .
  • Walls , DF . 1983 . Nature , 306 : 141 – 146 .
  • Yuen , HP . 1976 . Phys. Rev. A , 13 : 2226 – 2243 .
  • Teich , MC and Saleh , BEA . 1989 . Quantum Opt. , 1 : 153 – 191 .
  • Bužek , V . 1990 . J. Mod. Opt. , 37 : 303 – 316 .
  • Fan , HY . 2003 . J. Opt. B: Quantum Semiclass. Opt. , 59 : R147 – R163 . Fan, H.Y.; Zaidi, H.R.; Klauder, J.R. Phys. Rev. D 1987, 35, 1831–1834; Fan, H.Y.; Fan, Y. Phys. Rev. A 1996, 54, 958–960.
  • Wunsche , A . 1999 . J. Opt. B: Quantum Semiclass. Opt. , 1 : R11 – R21 .
  • Fan , HY , Lu , HL and Fan , Y . 2006 . Ann. Phys. , 321 : 480 – 494 .
  • Boggess , A and Narcowich , FJ . 2002 . A First Course in Wavelets with Fourier Analysis , 255 – 260 . Beijing : Publishing House of Electronics Industry .
  • Erdelyi , A . 1953 . Higher Transcendental Functions, The Bateman Manuscript Project , New York : McGraw Hill .
  • Addison , PS . 2002 . The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance , London : Institute of Physics Publishing .
  • Antoine , P , Piraux , B and Maquet , A . 1995 . Phys. Rev A , 51 : R1750 – R1753 .
  • De Luca , S and Fiordilino , E . 1996 . J. Phys. B: At. Mol. Opt. Phys. , 29 : 3277 – 3292 .
  • Terraneo , M , Georgeot , B and Shepelyansky , DL . 2005 . Phys. Rev. E , 71 : 066215 – 066228 .
  • Terraneo , M and Shepelyansky , DL . 2003 . Phys. Rev. Lett. , 90 : 257902 – 257905 .
  • Tymczak , CJ and Wang , XQ . 1997 . Phys. Rev. Lett. , 78 : 3654 – 3657 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.