1. High-precision evaluation of Wigner's d-matrix by exact diagonalization
- Author
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Feng, X. M., Wang, P., Yang, W., and Jin, G. R.
- Subjects
Quantum Physics ,Mathematical Physics ,Nuclear Theory ,Physics - Atomic Physics ,Physics - Computational Physics - 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 $100$., Comment: 4 pages, 3 figures; a Fortran90 code is included; resubmitted to Phys. Rev. E
- Published
- 2015
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