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projective quantum numbers


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1: 34.10 Zeros
In a 3 j symbol, if the three angular momenta j 1 , j 2 , j 3 do not satisfy the triangle conditions (34.2.1), or if the projective quantum numbers do not satisfy (34.2.3), then the 3 j symbol is zero. …However, the 3 j and 6 j symbols may vanish for certain combinations of the angular momenta and projective quantum numbers even when the triangle conditions are fulfilled. …
2: 34.2 Definition: 3 j Symbol
The corresponding projective quantum numbers m 1 , m 2 , m 3 are given by …
See accompanying text
Figure 34.2.1: Angular momenta j r and projective quantum numbers m r , r = 1 , 2 , 3 . Magnify
3: Bibliography C
  • L. Carlitz (1953) Some congruences for the Bernoulli numbers. Amer. J. Math. 75 (1), pp. 163–172.
  • F. Cooper, A. Khare, and U. Sukhatme (1995) Supersymmetry and quantum mechanics. Phys. Rep. 251, pp. 267–385.
  • J. Crisóstomo, S. Lepe, and J. Saavedra (2004) Quasinormal modes of the extremal BTZ black hole. Classical Quantum Gravity 21 (12), pp. 2801–2809.
  • Cunningham Project (website)
  • H. L. Cycon, R. G. Froese, W. Krisch, and B. Simon (2008) Schrödinger Operators, with Applications to Quantum Mechanics and Global Geometry. Springer Verlag, New York.
  • 4: Bibliography B
  • L. E. Ballentine and S. M. McRae (1998) Moment equations for probability distributions in classical and quantum mechanics. Phys. Rev. A 58 (3), pp. 1799–1809.
  • M. V. Berry and F. J. Wright (1980) Phase-space projection identities for diffraction catastrophes. J. Phys. A 13 (1), pp. 149–160.
  • H. A. Bethe and E. E. Salpeter (1957) Quantum mechanics of one- and two-electron atoms. Springer-Verlag, Berlin.
  • H. A. Bethe and E. E. Salpeter (1977) Quantum Mechanics of One- and Two-electron Atoms. Rosetta edition, Plenum Publishing Corp., New York.
  • L. C. Biedenharn and J. D. Louck (1981) Angular Momentum in Quantum Physics: Theory and Application. Encyclopedia of Mathematics and its Applications, Vol. 8, Addison-Wesley Publishing Co., Reading, M.A..
  • 5: Bibliography D
  • G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris (1994) Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.
  • P. Dean (1966) The constrained quantum mechanical harmonic oscillator. Proc. Cambridge Philos. Soc. 62, pp. 277–286.
  • P. Deligne, P. Etingof, D. S. Freed, D. Kazhdan, J. W. Morgan, and D. R. Morrison (Eds.) (1999) Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2. American Mathematical Society, Providence, RI.
  • K. Dilcher (1996) Sums of products of Bernoulli numbers. J. Number Theory 60 (1), pp. 23–41.
  • K. Dilcher (2002) Bernoulli Numbers and Confluent Hypergeometric Functions. In Number Theory for the Millennium, I (Urbana, IL, 2000), pp. 343–363.