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\(\newcommand{\PB}[1]{[#1]_\text{PB}}\)
Compute the Poisson brackets of components of angular momentum \(\vec{L}\) and show that
- \( [L_j, x_k]_\text{PB} =\epsilon_{jk\ell}\, x_\ell \)
- \( [L_j, p_k]_\text{PB} = \epsilon_{jk\ell}\, p_\ell \)
- \([L_j, \vec{p}^{\,2}]_\text{PB} =0 \)
- \([L_j, f(r,p)]_\text{PB}=0\)
Here \(f\) is an arbitrary function of \(r=|\vec{x}|\) and ,\(p=|\vec{p}|\).
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4727:Diamond Point
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