Skip to main content
SpringerLink
Log in

New Two-Mode Canonical Operator Realization of Angular Momentum and Generalized Fractional Fourier Transformation Obtained via Entangled State Representation

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

By virtue of two mutually conjugate bipartite entangled state representations |η〉 and |ξ〉 (Fan and Klauder, Phys Rev A 49:704, 1994) we find new canonical operator realization (COR) of angular momentum. As its two applications, we point out that the COR helps to develop Schwinger bosonic realization theory, and can generalize the concept of FrFT, i.e., constructing new 2-dimensioanl fractional Fourier transformation with additivity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fan, H.-y., Klauder, J.R.: Eigenvectors of two particles’ relative position and total momentum. Phys. Rev. A 49, 704 (1994)

    Article  ADS  MATH  Google Scholar 

  2. Fan, H.-y., Chen, B.-z.: Density matrix for a triatomic linear molecule model. Phys. Rev. A 50, 3754 (1994)

  3. Fan, H.-y., Ye, X.: Common eigenstates of two particles’ center-of-mass coordinates and mass-weighted relative momentum. Phys. Rev. A 51, 3343 (1995)

  4. Schwinger, J.: Quantum Theory of Angular Momentum. Academic Press, New York (1965)

    Google Scholar 

  5. Holstein, T., Primakoff, H.: Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys. Rev. 58, 1098 (1940)

    Article  ADS  MATH  Google Scholar 

  6. Fan, H.-y., Chen, J.-h.: Atomic coherent states studied by virtue of the EPR entangled state and their Wigner functions. Eur. Phys. J. D 23, 437 (2003)

    Article  ADS  Google Scholar 

  7. Namias, V.: J. Inst. Math. Appl. 25, 241–265 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mendlovic, D., Ozaktas, H.M., Lohmann, A.W.: Graded-index fibers, Wigner-distribution function, and the fractional Fourier transform. Appl. Opt. 33, 6188–6193 (1994)

    Article  ADS  Google Scholar 

  9. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  10. Fan, H.-Y., Lu, H.-L., Fan, Y.: Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations. Ann. Phys 321, 480 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Fan, H.Y., Fan, Y.: Representations of two-mode squeezing transformations. Phys. Rev. A 54, 958 (1996)

    Article  Google Scholar 

  12. Loudon, R., Knight, P.L.: Squeezed light. J. Mod. Opt. 34, 709 (1987)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Perelomov, A.M.: Generalized Coherent States and Their Applications. Springer, Berlin (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Ningbo University, Ningbo, 315211, China

    Hong-yi Fan & Sen-yue Low

  2. Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui, 230026, China

    Jun-hua Chen

Authors
  1. Hong-yi Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun-hua Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sen-yue Low
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hong-yi Fan.

Additional information

Supported by and the National Natural Science Foundation of China under Grant No 11175113.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, Hy., Chen, Jh. & Low, Sy. New Two-Mode Canonical Operator Realization of Angular Momentum and Generalized Fractional Fourier Transformation Obtained via Entangled State Representation. Int J Theor Phys 53, 2827–2835 (2014). https://doi.org/10.1007/s10773-014-2080-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-014-2080-2

Keywords

Search

Navigation