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Volumn 92, Issue 1, 2004, Pages 104011-104014

Bohr-Sommerfeld Quantization of Spin Hamiltonians

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); EIGENVALUES AND EIGENFUNCTIONS; GREEN'S FUNCTION; HAMILTONIANS; TENSORS;

EID: 1242307268     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (20)

References (29)
  • 3
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    • Frontiers of Neutron Scattering, edited by A. Furrer (World-Scientific, Singapore)
    • See, e.g., the review by J. Villain, Molecular Magnetism: A School of Physics, in Frontiers of Neutron Scattering, edited by A. Furrer (World-Scientific, Singapore, 2000).
    • (2000) Molecular Magnetism: A School of Physics
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  • 9
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    • Springer-Verlag, Berlin; see Chap. 5
    • See, e.g., D.C. Mattis, The Theory of Magnetism (Springer-Verlag, Berlin 1981), Vol. I; see Chap. 5.
    • (1981) The Theory of Magnetism , vol.1
    • Mattis, D.C.1
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    • F. D. M. Haldane, Phys. Lett. A 93, 464 (1983); Phys. Rev. Lett. 50, 1153 (1983); J. Appl. Phys. 57, 3359 (1985).
    • (1983) Phys. Lett. A , vol.93 , pp. 464
    • Haldane, F.D.M.1
  • 11
    • 4244109353 scopus 로고
    • F. D. M. Haldane, Phys. Lett. A 93, 464 (1983); Phys. Rev. Lett. 50, 1153 (1983); J. Appl. Phys. 57, 3359 (1985).
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 1153
  • 12
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    • F. D. M. Haldane, Phys. Lett. A 93, 464 (1983); Phys. Rev. Lett. 50, 1153 (1983); J. Appl. Phys. 57, 3359 (1985).
    • (1985) J. Appl. Phys. , vol.57 , pp. 3359
  • 14
    • 1242291145 scopus 로고    scopus 로고
    • note
    • We regard a BS rule as proper only if it includes these corrections. For a single particle, e.g., the action for an orbit must be equated to (n + 1/2)(2πℏ), and the rule would be improper if the 1/2 were left out. The necessity and rationale for including these corrections is well known. In the spin case, we similarly require the 1/j corrections relative to leading order.
  • 16
    • 0034367834 scopus 로고    scopus 로고
    • M. Stone, K.-S. Park, and A. Garg, J. Math. Phys. (N.Y.) 41, 8025 (2000). See also H. G. Solari, ibid. 28, 1097 (1987); E. A. Kochetov, ibid. 36, 4667 (1995); V. R. Vieira and P. D. Sacramento, Nucl. Phys. B448, 331 (1995).
    • (2000) J. Math. Phys. (N.Y.) , vol.41 , pp. 8025
    • Stone, M.1    Park, K.-S.2    Garg, A.3
  • 17
    • 0010689918 scopus 로고
    • M. Stone, K.-S. Park, and A. Garg, J. Math. Phys. (N.Y.) 41, 8025 (2000). See also H. G. Solari, ibid. 28, 1097 (1987); E. A. Kochetov, ibid. 36, 4667 (1995); V. R. Vieira and P. D. Sacramento, Nucl. Phys. B448, 331 (1995).
    • (1987) J. Math. Phys. (N.Y.) , vol.28 , pp. 1097
    • Solari, H.G.1
  • 18
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    • M. Stone, K.-S. Park, and A. Garg, J. Math. Phys. (N.Y.) 41, 8025 (2000). See also H. G. Solari, ibid. 28, 1097 (1987); E. A. Kochetov, ibid. 36, 4667 (1995); V. R. Vieira and P. D. Sacramento, Nucl. Phys. B448, 331 (1995).
    • (1995) J. Math. Phys. (N.Y.) , vol.36 , pp. 4667
    • Kochetov, E.A.1
  • 19
    • 10444276836 scopus 로고
    • M. Stone, K.-S. Park, and A. Garg, J. Math. Phys. (N.Y.) 41, 8025 (2000). See also H. G. Solari, ibid. 28, 1097 (1987); E. A. Kochetov, ibid. 36, 4667 (1995); V. R. Vieira and P. D. Sacramento, Nucl. Phys. B448, 331 (1995).
    • (1995) Nucl. Phys. , vol.B448 , pp. 331
    • Vieira, V.R.1    Sacramento, P.D.2
  • 20
    • 1242336073 scopus 로고    scopus 로고
    • note
    • The degree of this polynomial can be no greater than 2j, but in physical situations it is usually much smaller.
  • 21
    • 85088489165 scopus 로고    scopus 로고
    • note
    • + is the area inside the orbit traversed in the counterclockwise sense.
  • 24
    • 1242291144 scopus 로고
    • Proceedings of the Les Houches Summer School, Session XXVIII, edited by R. Balian and J. Zinn-Justin (North-Holland, Amsterdam
    • This observation is originally due to L. D. Faddeev, in Methods in Field Theory, Proceedings of the Les Houches Summer School, Session XXVIII, edited by R. Balian and J. Zinn-Justin (North-Holland, Amsterdam, 1976); J. R. Klauder, Phys. Rev. D 19, 2349 (1979).
    • (1976) Methods in Field Theory
    • Faddeev, L.D.1
  • 25
    • 4243623661 scopus 로고
    • This observation is originally due to L. D. Faddeev, in Methods in Field Theory, Proceedings of the Les Houches Summer School, Session XXVIII, edited by R. Balian and J. Zinn-Justin (North-Holland, Amsterdam, 1976); J. R. Klauder, Phys. Rev. D 19, 2349 (1979).
    • (1979) Phys. Rev. D , vol.19 , pp. 2349
    • Klauder, J.R.1
  • 27
    • 1242291148 scopus 로고    scopus 로고
    • note
    • Up to terms of order (1/j), this is equivalent to the rule as given in Ref. [11]. One can show this in the same way that we derive Eq. (34).
  • 28
    • 85088490037 scopus 로고    scopus 로고
    • 2jℓ)
    • 2jℓ)


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