title: High-precision evaluation of Wigner's d matrix by exact diagonalization.
abstract: The precise calculations of Wigner's d matrix are important in various research fields. Due to the presence of large numbers, direct calculations of the matrix using Wigner's formula suffer from a loss of precision. We present a simple method to avoid this problem by expanding the d matrix into a complex Fourier series and calculate the Fourier coefficients by exactly diagonalizing the angular momentum operator J(y) in the eigenbasis of J(z). This method allows us to compute the d matrix and its various derivatives for spins up to a few thousand. The precision of the d matrix from our method is about 10(-14) for spins up to 100.
authors.affiliation: Department of Physics, Beijing Jiaotong University, Beijing 100044, China.
authors.forename: X M
authors.initials: XM
authors.lastname: Feng
authors.affiliation: Beijing Computational Science Research Center, Beijing 100084, China.|Department of Modern Physics, Hefei National Laboratory for Physics Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: P
authors.initials: P
authors.lastname: Wang
authors.affiliation: Beijing Computational Science Research Center, Beijing 100084, China.
authors.forename: W
authors.initials: W
authors.lastname: Yang
authors.affiliation: Department of Physics, Beijing Jiaotong University, Beijing 100044, China.
authors.forename: G R
authors.initials: GR
authors.lastname: Jin