11,396 research outputs found
Wigner-Eckart theorem for tensor operators of Hopf algebras
We prove Wigner-Eckart theorem for the irreducible tensor operators for
arbitrary Hopf algebras, provided that tensor product of their irreducible
representation is completely reducible. The proof is based on the properties of
the irreducible representations of Hopf algebras, in particular on Schur lemma.
Two classes of tensor operators for the Hopf algebra U(su(2)) are
considered. The reduced matrix elements for the class of irreducible tensor
operators are calculated. A construction of some elements of the center of
U(su(2)) is given.Comment: 14 pages, late
Alternative sets of hyperspherical harmonics: Satisfying cusp conditions through frame transformations
By extending the concept of Euler-angle rotations to more than three
dimensions, we develop the systematics under rotations in higher-dimensional
space for a novel set of hyperspherical harmonics. Applying this formalism, we
determine all pairwise Coulomb interactions in a few-body system without
recourse to multipole expansions. Our approach combines the advantages of
relative coordinates with those of the hyperspherical description. In the
present method, each Coulomb matrix element reduces to the ``1/r'' form
familiar from the two-body problem. Consequently, our calculation accounts for
all the cusps in the wave function whenever an interparticle separation
vanishes. Unlike a truncated multipole expansion, the calculation presented
here is exact. Following the systematic development of the procedure for an
arbitrary number of particles, we demonstrate it explicitly with the simplest
nontrivial example, the three-body system.Comment: 19 pages, no figure
On the Clebsch-Gordan coefficients for the two-parameter quantum algebra
We show that the Clebsch - Gordan coefficients for the -
algebra depend on a single parameter Q = ,contrary to the explicit
calculation of Smirnov and Wehrhahn [J.Phys.A 25 (1992),5563].Comment: 5 page
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