Quantum Theory of Angular Momentum

By D. Mattis. 1981

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Citations in the corpus

On representing chemical environments (2012, background): “The factor in parentheses is the Wigner-3 jm symbol 43 , which is zero unless The numbers Q l and W l are called second-order and third-order bond-order parameters, respectively.”
Hidden pseudospin and spin symmetries and their origins in atomic nuclei (2014, methodology): “with the spherical harmonics spinor Y la jama(r̂) for the angular and spin parts [274].”
Fast estimation of polarization power spectra using correlation functions (2003, methodology): “Defining ξ−(β) ≡ 〈P̄ (n̂1)P̄ (n̂2)〉, (16) ξ+(β) ≡ 〈P̄ ∗(n̂1)P̄ (n̂2)〉, (17) ξX(β) ≡ 〈T (n̂1)P̄ (n̂2)〉, (18) we have 〈Q̄(n̂1)Q̄(n̂2)〉 = 1 2 [ξ+(β) + ℜξ−(β)], (19) 〈Ū(n̂1)Ū(n̂2)〉 = 1 2 [ξ+(β) −ℜξ−(β)], (20) 〈Q̄(n̂1)Ū(n̂2)〉 = 1 2 ℑξ−(β), (21) 〈T (n̂1)Q̄(n̂2)〉 = ℜξX(β), (22) 〈T (n̂1)Ū(n̂2)〉 =…”
The pre-launch Planck Sky Model: a model of sky emission at submillimetre to centimetre wavelengths (2012, methodology): “Transform the harmonic coefficients of the unlensed CMB fields and of the displacement field into their 2-d torus Fourier counterparts using the symmetry and recursion relation of the Wigner rotation matrix (Varshalovich et al. 1988; Challinor & Lewis 2005); 3.”
Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials (2014, background): “When the rotation is parameterized in terms of the three Euler angles, these functions are better known as D m,m′(α, β, γ), the Wigner D-functions, which form the representations of the SO(3) rotational group [9, 8].”
SE(3)-equivariant prediction of molecular wavefunctions and electronic densities (2021, unknown): “whereC321 m3,m2,m1 are Clebsch-Gordan coefficients (CGCs) [55].”
Calculating anisotropic physical properties from texture data using the MTEX open-source package (2011, background): “The estimation of physical properties of crystalline aggregates from the properties of the component crystals has been subject of extensive literature since the classical work of Voigt (1928) and Reuss (1929).”
On meson resonances and chiral symmetry (2003, unknown): “where we introduced parity eigenstates with 〈1±, J | = (±〈+1, J |+〈−1, J |)/ √ 2 and applied the useful identities [38]”
Relativistic continuum Hartree Bogoliubov theory for ground-state properties of exotic nuclei (2005, background): “with Gα(r)/r and F κ α (r)/r the radial wave functions for the upper and lower components and Y l jm(θ, φ) the spinor spherical harmonics [67].”
CMB Lensing Reconstruction on the Full Sky (2003, background): “(11) The integral can be performed analytically using the relation [20]”