Zeitschrift für Physik B Condensed Matter

, Volume 21, Issue 3, pp 313–318 | Cite as

On the general linear (Bogoliubov-) transformation for bosons

  • W. Witschel


Using a Baker-Campbell-Hausdorff formula for the disentangling of exponential operators, a simple straight-forward derivation of Bogoliubov-transformation matrix elements could be given by elementary algebra. Recent much more complicated derivations by means of hypergeometric functions are simplified considerably. Matrix elements and their generating functions are new for the general linear transformation for bosons. The surprising result of Aronsonet al., that the linear transformation matrix element is equivalent to the rotation matrix element is discussed in the framework of the coupled boson theory of angular momentum. Possible applications of the formalism for quantum optics and for nuclear models are sketched briefly.


Neural Network Generate Function Matrix Element Angular Momentum Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bogoliubov, N.N.: J. Phys. (USSR)11, 77 (1947)Google Scholar
  2. 2.
    Bassichis, W.H., Foldy, L.L.: Phys. Rev.133, A 935 (1964)Google Scholar
  3. 3.
    Salomon, A.I.: J. Math. Phys.12, 390 (1971)Google Scholar
  4. 4.
    Tanabe, K.: J. Math. Phys.14, 618 (1973)Google Scholar
  5. 5.
    Aronson, E.B., Malkin, I.A., Man'ko, V.I.: Lett. Nuovo Cim.11, 44 (1974)Google Scholar
  6. 6.
    Malkin, I.A., Man'ko, V.I., Trifonov, D.A.: J. Math. Phys.14, 576 (1973)Google Scholar
  7. 7.
    Witschel, W.: J. Phys. A: Math., Nucl., Gen.7, 1847 (1974)Google Scholar
  8. 8.
    Wilcox, R.M.: J. Math. Phys.8, 962 (1967)Google Scholar
  9. 9.
    Gilmore, R.: J. Math. Phys.15, 2090 (1974)Google Scholar
  10. 10.
    Messiah, A.: Quantum Mechanics I, pp. 454–457. Amsterdam: North Holland 1964Google Scholar
  11. 11.
    Lehrer-Ilamed, Y.: Proc. Camb. Phil. Soc.60, 61 (1964)Google Scholar
  12. 12.
    Schwinger, J.: On angular momentum, in: Quantum theory of angular momentum edited by Biedenharn, L.C., van Dam, H. New York: Academic Press 1965Google Scholar
  13. 13.
    Edmonds, A.R.: Drehimpulse in der Quantenmechanik. Mannheim: Bibliogr. Inst. 1964Google Scholar
  14. 14.
    Miller, W.: Lie theory and special functions. New York: Academic Press 1968Google Scholar
  15. 15.
    Goshen, S., Lipkin, H.J.: On the application of the groupSp(4) orR(5) to nuclear structure, in: Spectroscopic and group theoretical methods in physics. Amsterdam: North Holland 1968Google Scholar
  16. 16.
    Tanabe, K., Sugawara-Tanabe, K.: Phys. Letters B34, 575 (1971)Google Scholar
  17. 17.
    Sack, R.A.: Phil. Mag.3, 497 (1958)Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • W. Witschel
    • 1
  1. 1.Institut für Physikalische ChemieTechnische Universität BraunschweigBraunschweigFederal Republic of Germany

Personalised recommendations