Related papers: COMBINATORIAL COMPUTATION OF CLEBSCH-GORDAN COEFFI…
This article presents the derivation of a comprehensive formula for the Clebsch-Gordan coefficients in a quantum system. The formula is derived by employing the iterative application of angular momentum ladder operators on each defined…
A particular case of degenerate Clebsch-Gordan coefficient can be expressed with three binomial coefficients. Such a formula, which may be obtained using the standard ladder operator procedure, can also be derived from the Racah-Shimpuku…
We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin…
Fast, accurate, and stable computation of the Clebsch-Gordan (C-G) coefficients is always desirable, for example, in light scattering simulations, the translation of the multipole fields, quantum physics and chemistry. Current recursive…
Angular momentum in classical and quantum mechanics is carried out beyond textbooks frames. We compare angular distribution of particle position with classical probabilistic approach. Addition of angular momenta is also discussed together…
We present a mathematical proof of the algorithm allowing to generate all - symmetric and non-symmetric - total angular momentum eigenstates in remote matter qubits by projective measurements, proposed in Maser et al. [Phys. Rev. A 79,…
A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version…
The Proca-Corben-Schwinger equations for a spin-1 particle with an anomalous magnetic moment are added by a term describing an electric dipole moment, then they are reduced to a Hamiltonian form, and finally they are brought to the…
A class of Clebsch-Gordan coefficients are derived from the properties of conditional probability using the binomial distribution. In particular, in the case of $l=l_1+l_2$ it is shown that $$[<l_1/2-k_1, l_2/2-k_2|l/2, k=k_1+k_2]>^2…
Given standard angular momentum and boost matrices, the commutation rules for vector and momentum matrices are solved. The resulting matrix components are displayed as detailed functions of spin with factors such as the square root of…
A theory of Clebsch-Gordan coefficients for $SL(2, C)$ is given using only rational numbers. Features include orthogonality relations, recurrence relations, and Regge's symmetry group. Results follow from elementary representation theory…
In the study of the amplitudes for many-particle processes, and also for processes involving particles with spin, the use is made of matrix elements of the rotation group d^j_{\mu\nu}(z). In this paper the generalization of the functions…
A numerical algorithm that computes the decomposition of any finite-dimen\-sio\-nal unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight on the group structure, is…
A new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta of the relative displacements of particle…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
Two-phase composites with non-overlapping inclusions randomly embedded in matrix are investigated. A straight forward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value…
The spin of a composite particle, like a nucleus or a hadron, is generated by the composition of angular moments (consisting of spins and orbital angular moments) of the constituents. The composition of two angular moments is done by the…
We obtain exact, simple and very compact expressions for the linearization coefficients of the products of orthogonal polynomials; both the conventional Clebsch-Gordan-type and the modified version. The expressions are general depending…
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order…
Asymptotic expressions for Clebsch-Gordan coefficients are derived from an exact integral representation. Both the classically allowed and forbidden regions are analyzed. Higher-order approximations are calculated. These give, for example,…