Simplified recursive algorithm for Wigner [formula presented] and [formula presented] symbols

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 6, 1998, Pages 7274-7277

  Luscombe, James H ^a   Luban, Marshall ^b  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11544316294     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.7274     Document Type: Article

References (11)

1. E. P. Wigner, Group Theory (Academic Press, New York, 1959), p. 191
2. G. Racah, Phys. Rev. 62, 438 (1942).
3. A useful summary of the 3j and 6j symbols and the Wigner-Racah formulas is given by A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1962), Vol. II, Appendix C.
4. K. Schulten and R. G. Gordon, J. Math. Phys. 16, 1961 (1975). While the various three-term recurrence relations satisfied by the 3j and 6j symbols have been derived previously by several authors, Schulten and Gordon provide a useful, unified derivation of these recurrence relations.JMAPAQ
5. Semiclassical approximations are discussed in detail by G. Ponzano and T. Regge, in Spectroscopic and Group Theoretical Methods in Physics, edited by F. Bloch et al. (North-Holland, Amsterdam, 1968), pp. 1–58.
6. Additional semiclassical results are derived by K. Schulten and R. G. Gordon, J. Math. Phys. 16, 1971 (1975).
7. Early work on the classical limits of the 3j and 6j symbols includes that of Wigner 1, Chap. 27
8. P. J. Brussaard and H. A. Tolhoek, Physica (Amsterdam) 23, 955 (1957).PHYSAG
9. For many quantum-mechanically allowed 3j and 6j symbols, there do not exist vector diagrams showing the coupling of the angular momentum vectors. For example, consider (02j jj -jj); this is but one example of a well-defined 3j symbol [of value (2j)!/(4j+1)!] for which a vector addition diagram does not exist (for j>12). The “classical region” of the 3j and 6j symbols is defined as the set of quantum numbers for which vector diagrams do exist.
10. See, for example, the discussion given by M. Luban and J. H. Luscombe, Phys. Rev. B 35, 9045 (1987)
11. and by W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge University Press, Cambridge, England, 1992), pp. 179–181.