, Volume 11, Issue 1, pp 85–99 | Cite as

The Heisenberg ferromagnet in spin coherent state representation

  • B Sriram Shastry
  • G S Agarwal
  • I Rama Rao


A new approach to Heisenberg ferromagnet using the spin coherent state representation is developed. The differential operator representation of spin angular momentum operators is used to derive thec-number analogs of the basic quantum mechanical equations, viz., the Schrödinger, Bloch and Liouville equations for the Heisenberg ferromagnet. As an important illustration of our formulation, which has noad hoc assumptions and does not use any boson representation, the excitation spectrum for one, two and three spin waves is obtained. In these cases it is also shown that eigenvalue spectrum can be obtained by completely ignoring the kinematical interactions.


Heisenberg ferromagnet spin coherent states 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Agarwal G S 1969Phys. Rev. 177 400CrossRefADSMathSciNetGoogle Scholar
  2. Agarwal G S 1973Progress in Optics ed E Wolf (Amsterdam: North Holland) Vol. 11, p. 1.Google Scholar
  3. Akhiezer A I, Baryakhtar V V and Peletiminiskii S V 1969Spin Waves translated by S Chomet (Amsterdam: North Holland)Google Scholar
  4. Arecchi F T, Courtens E, Gilmore R and Thomas H 1972Phys. Rev. A6 2211ADSGoogle Scholar
  5. Balakrishnan V 1975Phys. Rev. B11 256ADSGoogle Scholar
  6. Biswas A C and Rama Rao I 1971Physica 53 493CrossRefADSGoogle Scholar
  7. Biswas A C and Rama Rao I 1973Physica 65 412CrossRefADSGoogle Scholar
  8. De Ciorgio V and Scully M O 1970Phys. Rev. A2 1170ADSGoogle Scholar
  9. Douglass K H 1971Ann. Phys. 62 383CrossRefADSMathSciNetGoogle Scholar
  10. Douglass K H 1971Ann. Phys. 64 396CrossRefADSMathSciNetGoogle Scholar
  11. Dyson F J 1956aPhys. Rev. 102 1217MATHCrossRefADSMathSciNetGoogle Scholar
  12. Dyson F J 1956bPhys. Rev. 102 1230MATHCrossRefADSMathSciNetGoogle Scholar
  13. Fakuda N and Wortis M 1963J. Phys. Chem. Solids 24 1675CrossRefADSGoogle Scholar
  14. Gilmore R 1976J. Phys. A9 L65Google Scholar
  15. Gilmore R, Bowden C M and Narducci L M 1975Phys. Rev. A12 1019ADSGoogle Scholar
  16. Graham R and Haken H 1970Z. Phys. 237 31CrossRefADSMathSciNetGoogle Scholar
  17. Haake F 1973Springer Tracts in Modern Physics (New York: Springer-Verlag) Vol. 66, p. 98Google Scholar
  18. Haken H 1970Laser Theory Handbuch der Phys. (New York: Springer-Verlag), Vol. 25/2cGoogle Scholar
  19. Haken H 1975Rev. Mod. Phys. 47 67CrossRefADSMathSciNetGoogle Scholar
  20. Kutzner J 1973Z. Phys. 259 177CrossRefADSMathSciNetGoogle Scholar
  21. Langer J S 1968Phys. Rev. 167 183CrossRefADSGoogle Scholar
  22. Langer J S 1969Phys. Rev. 184 219CrossRefADSGoogle Scholar
  23. Lugiato L A, Narducci L M and Gronchi M 1977Phys. Rev. A15 1126ADSGoogle Scholar
  24. Majumdar C K 1969J. Math. Phys. 10 177CrossRefADSMathSciNetGoogle Scholar
  25. Majumdar C K, Mukhopadhya G and Rajagopal A K 1973Pramana 1 135ADSCrossRefGoogle Scholar
  26. Maleev S V 1958Sov. Phys. JETP 6 776ADSGoogle Scholar
  27. Pushkarov D I and Pushkarov K H I 1977Phys. Stat. Solidi B81 703CrossRefGoogle Scholar
  28. Radcliffe J M 1971J. Phys. A4 313ADSMathSciNetGoogle Scholar
  29. Rogovin D, Scully M O and Lee P A 1973Progress in Quantum Electronics 215Google Scholar
  30. Rama Rao I and Rajagopal A K 1977Phys. Rev. B16 3148ADSGoogle Scholar
  31. Scott J F, Sargent M III and Cantroll C D 1975Opt. Commun. 15 13CrossRefADSGoogle Scholar
  32. Shastry B S 1977 UnpublishedGoogle Scholar
  33. Takahashi Y and Shibata Y 1976J. Stat. Phys. 14 49CrossRefADSGoogle Scholar
  34. Tjon J and Wright J 1977Phys. Rev. B15 3470ADSGoogle Scholar
  35. Vilenkin N J 1968Special Functions and the Theory of Group Representations (American Math. Society) Chap. III section 2Google Scholar

Copyright information

© the Indian Academy of Sciences 1977

Authors and Affiliations

  • B Sriram Shastry
    • 1
  • G S Agarwal
    • 1
  • I Rama Rao
    • 1
    • 2
  1. 1.School of PhysicsUniversity of HyderabadHyderabad
  2. 2.Tata Institute of Fundamental ResearchBombay

Personalised recommendations