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High-precision evaluation of Wigner's d matrix by exact diagonalization.
1Department of Physics, Beijing Jiaotong University, Beijing 100044, China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
Summary
Precise Wigner d-matrix calculations are crucial. A new Fourier series method enhances accuracy for large spins, achieving 10(-14) precision for spins up to 100, overcoming limitations of direct Wigner formula computations.
Area of Science:
- Quantum mechanics
- Mathematical physics
- Computational physics
Background:
- Wigner's d matrix is essential for quantum mechanics and related fields.
- Direct computation using Wigner's formula faces precision issues with large numbers.
Purpose of the Study:
- To develop a precise and efficient method for calculating Wigner's d matrix.
- To overcome the precision limitations of existing Wigner's d matrix calculation methods.
Main Methods:
- Expansion of the d matrix into a complex Fourier series.
- Calculation of Fourier coefficients via exact diagonalization of the angular momentum operator J(y) in the eigenbasis of J(z).
Main Results:
- The proposed method achieves high precision (approx. 10(-14)) for Wigner d matrices.
- The method is effective for spins up to 100 and can be extended to a few thousand.
- Enables computation of the d matrix and its derivatives.
Conclusions:
- The Fourier series method offers a robust solution for accurate Wigner d-matrix computation.
- This approach significantly improves precision compared to direct Wigner formula calculations.
- The method is suitable for applications requiring high-accuracy Wigner d-matrix values, especially for large spin systems.
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