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Algebraic Realization of the Rotor

  • J. P. Draayer
  • Yorck Leschber

Abstract

The rotor enjoys a prominent place in physics. In classical mechanics it is usually offered as the most challenging example of rigid-body motion.1 Applications extend from the simple symmetrical top to the dynamics of mechanical gyros, satellite behavior, and even planetary motion. All physicists learn early in their career that “the polhode rolls on the herpolhode...”!

Keywords

Irreducible Representation Rotor Dynamic Symmetry Type Collective Model Inertia Parameter 
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.

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References

  1. 1.
    F. Klein and A Sommerfeld, “Theorie des Kreisels,” Volumes 1–4, Teubner, Leipzig (1897–1910);Google Scholar
  2. H. Goldstein, “Classical Mechanics,” Addison-Wesley Reading, Massachusetts (1980).Google Scholar
  3. 2.
    D. M. Dennison, Phys. Rev. 28: 318 (1926);CrossRefGoogle Scholar
  4. F. Reiche and H. Rademacher, Zeits. f. Physik 39:444 (1926); 41: 453 (1927);Google Scholar
  5. R. L. Kronig and I. I. Rabe, Phys. Rev. 29: 262 (1927);CrossRefGoogle Scholar
  6. C. Manneback, Phys. Zeits. 28: 72 (1927).Google Scholar
  7. 3.
    A. R. Edmonds, “Angular Momentum in Quantum Mechanics,” Princeton, New Jersey (1957).Google Scholar
  8. 4.
    E. Witmer, Proc. Nat. Acad. 13: 60 (1927);CrossRefGoogle Scholar
  9. S. C. Wang, Phys. Rev. 34: 243 (1929);CrossRefGoogle Scholar
  10. H. A. Kramers and G. P. Ittmann, Zeits. f. Physik 53:553 (1929); 58:217 (1929); 60: 663 (1930);Google Scholar
  11. O. Klein, Zeits. f. Physik 58: 730 (1929).CrossRefGoogle Scholar
  12. 5.
    R. S. Mulliken, Rev. Mod. Phys. 3: 89 (1931);CrossRefGoogle Scholar
  13. D. M. Dennison, Rev. Mod. Phys. 3: 280 (1930).CrossRefGoogle Scholar
  14. 6.
    R. S. Mulliken, Phys. Rev. 59: 873 (1941);CrossRefGoogle Scholar
  15. G. W. King, R. M. Hainer, and P. C. Cross, J. Chem. Phys. 11: 27 (1943);CrossRefGoogle Scholar
  16. C. H. Townes and A. L. Schawlow, “Microwave Spectroscopy,” McGraw-Hill, New York (1955).Google Scholar
  17. 7.
    H. B. G. Casimir, “Rotation of a Rigid Body in Quantum Mechanics,” J. B. Wolter’s, The Hague (1931).Google Scholar
  18. 8.
    A. Bohr and B. R. Mottelson, Phys. Rev. 89:316 (1953); 90: 717 (1953).CrossRefGoogle Scholar
  19. 9.
    A. Faessler, W. Greiner, and R. K. Sheline, Nucl. Phys. 70: 33 (1965).CrossRefGoogle Scholar
  20. 10.
    J. M. Eisenberg and W. Greiner, “Nuclear Theory,” Volumes 1, 2, and 3, North-Holland, Amsterdam (1975–1976);Google Scholar
  21. A. Bohr and B. Mottelson, “Nuclear Structure,” Volumes I and II, Benjamin, Reading, Massachusetts (1969–1975).Google Scholar
  22. 11.
    M. G. Mayer, Phys. Rev. 75:1969 (1949); 78: 16 (1950);Google Scholar
  23. O. Haxel, J. H. D. Jensen, and H. Suess, Phys. Rev. 75: 1766 (1949);CrossRefGoogle Scholar
  24. O. Haxel, J. H. D. Jensen, and H. Suess, Zeits. f. Physik 128: 295 (1950).CrossRefGoogle Scholar
  25. 12.
    D. L. Hill and J. A. Wheeler, Phys. Rev. 89: 1102 (1953).CrossRefGoogle Scholar
  26. 13.
    J. P. Elliott, Proc. Roy. Soc. A245: 128, 562 (1958).Google Scholar
  27. 14.
    A. Arima and F. Iachello, Ann. of Phys. 99:253 (1976); 111:201 (1978); 123: 468 (1979).Google Scholar
  28. 15.
    G. Rosensteel and D. J. Rowe, Ann. of Phys. 123:36 (1979); 126: 198, 343 (1980).Google Scholar
  29. 16.
    J. P. Elliott and M. Harvey, Proc. Roy. Soc. A272: 557 (1963);CrossRefGoogle Scholar
  30. J. P. Elliott and C. E. Wilsdon, Proc. Roy. Soc. A302: 509 (1968).CrossRefGoogle Scholar
  31. 17.
    R. D. Ratna Raju, J. P. Draayer and K. T. Hecht, Nucl. A202: 433 (1973).Google Scholar
  32. 18.
    A. S. Davydov and G. F. Fillippov, Nucl. Phys. 8: 237 (1958);CrossRefGoogle Scholar
  33. A. S. Davydov and A. A. Chaban, Nucl. Phys. 20: 499 (1960);CrossRefGoogle Scholar
  34. J. P. Davidson, Nucl. Phys. 33: 664 (1962);CrossRefGoogle Scholar
  35. J. P. Davidson, Rev. Mod. Phys. 37: 105 (1965);CrossRefGoogle Scholar
  36. A. S. Davydov, “Quantum Mechanics,” NEO Press, Ann Arbor, Michigan (1966).Google Scholar
  37. 19.
    A. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 26:No. 14 (1952);Google Scholar
  38. A. Bohr and B. R. Mottelson, Mat. Fys. Medd. Dan. Vid. Selsk. 27: No. 16 (1953);Google Scholar
  39. C. Marty, Nucl. Phys. 1:58 (1956); 3: 193 (1957).CrossRefGoogle Scholar
  40. 20.
    S. A. Williams, Nucl. Phys. 63: 581 (1965).CrossRefGoogle Scholar
  41. 21.
    G. Racah, Group Theory and Spectroscopy, in: CERN reprint of lectures delivered at the Institue for Advanced Study, Princeton, New Jersey (1951);Google Scholar
  42. G. Racah, Lectures on Lie Groups, in: “Farkas Memorial Volume,” A. Farkas and E. P. Wigner, eds., Research Council of Israel, Jerusalem (1952);Google Scholar
  43. G. Racah and I. Talmi, Phys. Rev. 89: 913 (1953).Google Scholar
  44. 22.
    R. N. Sen, “Construction of Irreducible Representations of SU(3),” Thesis, Hebrew University, Jerusalem (1963).Google Scholar
  45. 23.
    L. C. Biedenharn, Phys. Lett. 28B: 537 (1969);CrossRefGoogle Scholar
  46. J. A. Castilho Alcaras, L. C. Biedenharn, K. T. Hecht, and G. Neely, Ann. Phys. 60: 85 (1970);CrossRefGoogle Scholar
  47. J. W. B. Hughes, J. Phys. A6: 48, 281 (1973);Google Scholar
  48. M. Moshinsky, J. Patera, R. T. Sharp, and P. Winternitz, Ann. Phys. 95: 139 (1975);CrossRefGoogle Scholar
  49. H. E. DeMeyer, G. Vanden Berghe, J. W. B. Hughes, J. Math. Phys. 22:2360,2366 (1981); 24: 1025 (1983).Google Scholar
  50. 24.
    D. M. Brink and G. R. Satchler, “Angular Momentum,” Clarendon Press, Oxford (1962).Google Scholar
  51. 25.
    T. Molien, Preuss. Akad. Wiss. Sitzungberichte 1152 (1897);Google Scholar
  52. E. Noether, Math. Ann. 77: 89 (1916);CrossRefGoogle Scholar
  53. H. Weyl, “The Classical Groups,” Princeton, New Jersey (1946).Google Scholar
  54. 26.
    B. R. Judd, W. Miller Jr., J. Patera, and P. Winternitz, J. Math. Phys. 15: 1787 (1974).CrossRefGoogle Scholar
  55. 27.
    J. P. Draayer, Spectroscopy from the Bottom Up, in: “VIII Symposium on Nuclear Physics,” Proceedings, Institute de Fisica, U.N.A.M., Oaxtepec, Morelos, Mexico (1985).Google Scholar
  56. 28.
    Y. Leschber and J. P. Draayer, Phys. Rev. C33: 749 (1986).Google Scholar
  57. 29.
    J. P. Draayer and G. Rosensteel, Nucl. Phys. A439: 61 (1985).CrossRefGoogle Scholar
  58. 30.
    Y. Akiyama and J. P. Draayer, Comp. Phys. Comm. 5: 405 (1973).CrossRefGoogle Scholar
  59. 31.
    J. P. Draayer and K. J. Weeks, Ann. Phys. 156: 41 (1984).CrossRefGoogle Scholar
  60. 32.
    G. Racah, Rev. Mod. Phys. 21: 494 (1949);CrossRefGoogle Scholar
  61. J. P. Draayer and S. A. Williams, Nucl. Phys. A119: 577 (1968).CrossRefGoogle Scholar
  62. 33.
    J. P. Draayer and Y. Akiyama, J. Math. Phys. 14: 1904 (1973).CrossRefGoogle Scholar
  63. 34.
    J. P. Draayer, Algebraic Methods and the Microscopic/Macroscopic Connection for Nuclear Rotational Motion, in: “IX Symposium on Nuclear Physics,” Proceedings, Institute de Fisica, U.N.A.M., Oaxtepes, Morelos,Mexico (1986).Google Scholar
  64. 35.
    J. B. French, Phys. Lett. B26: 75 (1967);CrossRefGoogle Scholar
  65. F. S. Chang, J B. French, and T. H. Thio, Ann. of Phys. Ann. Phys. 66: 137 (1971).CrossRefGoogle Scholar
  66. 36.
    H. DeMeyer, G. Vanden Berghe, and J. Van der Jeugt, J. Math. Phys. 26: 3109 (1985).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • J. P. Draayer
    • 1
  • Yorck Leschber
    • 1
  1. 1.Department of Physics and AstronomyLouisiana State UniversityBaton RougeUSA

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