A General Graphical Method for Angular Momentum

Massot, Jean; Elbaz, E.; Lafoucrière, J.

doi:10.1103/revmodphys.39.288

Cited by 26 publications

(2 citation statements)

References 7 publications

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“…~U(~lrlal)U'(lczrzaz) (Icra) = 2 U;ylal) U ' ( k a r a a a ) yx (klk'PlP2 I kIk'kC1)YiYa }YOne verifies easily that the right hand side of relation(22) is cogredient with the U y ) operator. Note that:2 ~~(~~r~a~)~m~r~~~) ( k r a ) = 2 {~(~p z ) ) ?…”

mentioning

confidence: 69%

Energy levels of paramagnetic ions: Algebra. II

Kibler

1969

Int J of Quantum Chemistry

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AbstractsThe correspondence rules between the algebra of coupling coefficients of the special unitary group SU(2) and the associated algebra of a subgroup G of SU(2) are presented.'The matrix elements of the irreducible representations of G are written in a convenient quantization scheme and different relations between these matrix elements and the ClebschGordan coefficients of G are derived. Such a formalism is appropriate for numerous spectroscopic problems. As an example, it is applicd to crystal field theory and electron paramagnetic resonance. General formulas from which a large number of results are rederived and generalized in a straightforward fashion are given. Numerical values of coupling coefficients for the tetragonal and cubic groups are listed in the .4ppendix.O n Cnonce les regles pratiques de correspondance permettant de deduire I'algebre des coefficients de couplage d'un sous groupe fini G d u groupe unitaire special SU(2) a partir de celle de SU(2). Les

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confidence: 69%

Energy levels of paramagnetic ions: Algebra. II

Kibler

1969

Int J of Quantum Chemistry

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“…The Yutsis method maps the product structure of a Wigner 3n-j symbol onto a labeled 3-regular (also known as cubic) digraph [3,26,31,45]. Each factor is represented by a vertex.…”

Section: B Yutsis Reductionmentioning

confidence: 99%

The Wigner 3n-j Graphs up to 12 Vertices

Mathar¹

2011

Preprint

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On Invariants of the Rotation Group

Marinov¹,

Roginsky²

1971

Fortschr. Phys.

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Any quantity transforming according to an irreducible representation of the space rotation group may be realized in three forms: i) as a multispinor χ α 1…α2l; ii) as a 3‐tensor t i 1…il (for 2l even) or, tensor‐spinor t italicαi 1…il−1/2 (for 2l odd); iii) as an l‐spinor Ψλ(l) (λ = −l,…, l). Only one invariant may be constructed of three quantitites of a given kind; so the three invariants are equal up to a numerical factor that is found in the work. A number of invariants may be constructed of four quantities, not all of them independent. For applications it is of importance to be able to construct an independent set of invariants of every kind, as well as to relate the invariants of different kinds. This problem is solved in the present work for arbitrary angular momenta l1, l2, l3, l4.

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A General Graphical Method for Angular Momentum

Cited by 26 publications

References 7 publications

Energy levels of paramagnetic ions: Algebra. II

Energy levels of paramagnetic ions: Algebra. II

The Wigner 3n-j Graphs up to 12 Vertices

On Invariants of the Rotation Group

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