Abstract
By employing the technique of integral within an ordered product (IWOP) of operators we recast classical wavelet transform to a matrix element of the squeezing-displacing operator U(μ,s) between the mother wavelet vector 〈ψ| and the state vector |f〉 to be transformed, i.e., we propose that 〈ψ|U(μ,s)|f〉 can be considered as a new kind of spectrum for analyzing the quantum state |f〉. In this way we do numerical calculation of wavelet-transform spectrum for the even- and odd-coherent states and then plot their figures, respectively. Thus this kind of spectrum can be used to recognize a variety of quantum optical states.
Similar content being viewed by others
References
Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelphia (1992)
Chui, C.K.: An Introduction to Wavelets. Academic Press, New York (1992)
Jaffard, S., Meyer, Y., Ryan, R.D.: Wavelet, Tools for Science and Technology. SIAM, Philadelphia (2001)
Burrus, C.S., Gopinath, R.A., Guo, H.T.: Introduction to Wavelets and Wavelet Transformation (A Primer). Prentice-Hall, Prentice (1998)
Pinsky, M.A.: Introduction to Fourier Analysis and Wavelets. Book/Cole, Sydney (2002)
Hu, L.Y., Fan, H.Y.: Int. J. Theor. Phys. 48, 1539 (2009)
Rezaee, M., Jafarizadeh, M.A., Mirzaee, M.: Int. J. Quantum Inf. 5, 367 (2007)
Fan, H.Y.: J. Opt. B, Quantum Semiclass. Opt. 5, R147 (2003)
Fan, H.Y., Lu, H.L., Fan, Y.: Ann. Phys. 321, 480 (2006)
Fan, H.Y., Lu, H.L.: Opt. Lett. 31, 407 (2006)
Fan, H.Y., VanderLinde, J.: Phys. Rev. A 39, 1552 (1989)
Fan, H.Y., Zaidi, H.R., Klauder, J.R.: Phys. Rev. D 35, 1831 (1987)
Fan, H.Y., Zaidi, H.R.: Phys. Rev. A 37, 2985 (1988)
Klauder, J.R., Skargerstam, B.S.: Coherent States. Singapore, World Scientific (1985)
Glauber, R.J.: Quantum Theory of Optical Coherence. Wiley-VCH, Weinheim (2007)
Li, Y., Szu, H.H., Sheng, Y., Caufield, H.J.: Proc. IEEE 84, 720 (1996)
Roberge, D., Sheng, Y.: Appl. Opt. 33, 5287 (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Song, J., Fan, Hy. Wavelet Transform of Even- and Odd-Coherent States. Int J Theor Phys 49, 2582–2591 (2010). https://doi.org/10.1007/s10773-010-0449-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-010-0449-4