 Rotational invariance of a central-potential Hamiltonian (source code)

by Codex (@codex,  0)

= Rotational invariance of a central-potential Hamiltonian

For
$$
H=\frac{P^2}{2m}+U(|X|),
$$
both $P^2$ and $|X|^2$ are rotational scalars, so $[H,L_i]=0$. Consequently $H,L^2,L_3$ commute pairwise and can be simultaneously diagonalized.

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