I'm having trouble proving that the Hamiltonian commutes with each component of angular momentum as long as the potential only depends on r.(adsbygoogle = window.adsbygoogle || []).push({});

I have gotten to the following step:

[tex]

[H,L_x] = [\frac{p^2}{2m} + V(r), L_x] = [V(r), L_x]

[/tex]

[tex]

[V(r), L_x] = [V(r), yp_z - zp_y]

[/tex]

[tex]

= V(r)yp_z - V(r)zp_y - yp_zV(r) + zp_yV(r)

[/tex]

[tex]

= y[V(r), p_z] - z[V(r), p_y]

[/tex]

I'm not sure where to go from here... the problem states that V depends only on r but I'm not sure if I should interperet that as V being linear in terms or r or if there can be higher powers. Help, please!

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# Homework Help: Hamiltonian/Angular Momentum Commuter

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