projective quantum numbers

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1: 34.10 Zeros

… ►In a $\mathit{3}j$ 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 $\mathit{3}j$ symbol is zero. …However, the $\mathit{3}j$ and $\mathit{6}j$ 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: $\mathit{3}j$ Symbol

… ►The corresponding projective quantum numbers $m_1,m_2,m_3$ are given by … ►

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Figure 34.2.1: Angular momenta $j_r$ and projective quantum numbers $m_r$, $r=1,2,3$. Magnify

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3: Bibliography C

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Some congruences for the Bernoulli numbers. Amer. J. Math. 75 (1), pp. 163–172.

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External Links:

FullText, MathReview (A. L. Whiteman), ZentralBlatt

Referenced by:

§24.10(i).

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Supersymmetry and quantum mechanics. Phys. Rep. 251, pp. 267–385.

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Referenced by:

§18.38(iii).

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Quasinormal modes of the extremal BTZ black hole. Classical Quantum Gravity 21 (12), pp. 2801–2809.

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External Links:

ISSN 0264-9381, MathReview (Donato Bini), ZentralBlatt

Referenced by:

§13.28(iii).

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Notes:

Seeks to factor numbers of the form $b^n\pm 1$ for $b=2,3,5,6,7,10,11,12$.

External Links:

Home Page

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3rd item.

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Schrödinger Operators, with Applications to Quantum Mechanics and Global Geometry. Springer Verlag, New York.

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External Links:

ISBN 978-3-540-16758-7

Referenced by:

§1.18(vii), §1.18(x).

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4: Bibliography B

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Moment equations for probability distributions in classical and quantum mechanics. Phys. Rev. A 58 (3), pp. 1799–1809.

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External Links:

Document

Referenced by:

§24.18.

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Phase-space projection identities for diffraction catastrophes. J. Phys. A 13 (1), pp. 149–160.

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ISSN 0305-4470, Document, MathReview (J. S. Joel), ZentralBlatt

Referenced by:

§36.9.

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Quantum mechanics of one- and two-electron atoms. Springer-Verlag, Berlin.

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External Links:

MathReview (L. Van Hove), ZentralBlatt

Referenced by:

§18.39(ii), §18.39(ii).

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Quantum Mechanics of One- and Two-electron Atoms. Rosetta edition, Plenum Publishing Corp., New York.

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Notes:

Reprint (with corrections) of the original edition published in 1957 by Springer and Academic Press

External Links:

MathReview, ZentralBlatt (D. Geissler)

Referenced by:

§1.18(viii), §33.22(ii), §33.22(ii), §33.22(v).

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Angular Momentum in Quantum Physics: Theory and Application. Encyclopedia of Mathematics and its Applications, Vol. 8, Addison-Wesley Publishing Co., Reading, M.A..

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ISBN 0-201-13507-8, MathReview (Kurt Bernardo Wolf), ZentralBlatt

Referenced by:

§34.14.

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5: Bibliography D

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Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.

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External Links:

Document

Referenced by:

§13.28(iii).

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The constrained quantum mechanical harmonic oscillator. Proc. Cambridge Philos. Soc. 62, pp. 277–286.

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External Links:

Document, MathReview (T. Erber)

Referenced by:

§12.11(i), §12.11(i), §12.17.

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Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2. American Mathematical Society, Providence, RI.

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Notes:

Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997

External Links:

ISBN 0-8218-1198-3, MathReview, ZentralBlatt

Referenced by:

§21.9.

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Sums of products of Bernoulli numbers. J. Number Theory 60 (1), pp. 23–41.

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ISSN 0022-314X, Document, MathReview (Wen Peng Zhang), ZentralBlatt

Referenced by:

§24.14(ii).

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Bernoulli Numbers and Confluent Hypergeometric Functions. In Number Theory for the Millennium, I (Urbana, IL, 2000), pp. 343–363.

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External Links:

ISBN 1-56881-126-8, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.16(iii).

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