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## Main Question or Discussion Point

I know that in the case of central potential V(r) the hamiltonian of the system always commutes with l^2 operator. But what happends in this case?

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I know that in the case of central potential V(r) the hamiltonian of the system always commutes with l^2 operator. But what happends in this case?

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https://physics.stackexchange.com/questions/93533/commutator-of-l2-and-x2-p2

So put a particle in three dimensions to a field described by a harmonic oscillator potential, but only in the x-direction

##V(x,y,z) = ax^2##

That's not rotation invariant, but still commutes with the ##\hat{L}^2## (and hence the whole ##\hat{H}## commutes with ##\hat{L}^2##).

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