 Rotational invariance of a central-potential Hamiltonian

ID: rotational-invariance-of-a-central-potential-hamiltonian

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

H = \frac{P ^{2}}{2 m} + 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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