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arXiv · 1507.04535

High-precision evaluation of Wigner's d-matrix by exact diagonalization

X. M. Feng·P. Wang·W. Yang·G. R. Jin
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Abstract

The precise calculations of the Wigner's d-matrix are important in various research fields. Due to the presence of large numbers, direct calculations of the matrix using the Wigner's formula suffer from 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 $100$.

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X. M. Feng, P. Wang, W. Yang, G. R. Jin. 2015-10-05. High-precision evaluation of Wigner's d-matrix by exact diagonalization. https://doi.org/10.1103/physreve.92.043307

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