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# Operators commutation and relation between eigenfunctionseigenvalues

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# operators Operators commutation and relation between eigenfunctions

Good morning,

If H$$H$$ and L$$L_i$$ are commuting ( $$[H, L] = 0$$$$[H, L_i] = 0$$ ) could we deduce that the eigenvalues of H$$H$$ depend/ do not depend on m$$m$$ and l$$\ell$$ ( eigenvalue of $$L_z, L^2$$ )  ? I don't think so since it does not depend for the hydrogen atom but in a more general case could we deduce some relation between eigenvalues when two operators are commuting  ?

And in the particular case where H = $$L^2/2\mu a$$ $$H = L^2/2\mu a$$?

Thanks

# operators commutation and relation between eigenfunctions

Good morning,

If H and L are commuting ( $$[H, L] = 0$$ ) could we deduce that the eigenvalues of H depend/ do not depend on m and l ( eigenvalue of $$L_z, L^2$$ )  ? I don't think so since it does not depend for the hydrogen atom but in a more general case could we deduce some relation between eigenvalues when two operators are commuting  ?

And in the particular case where H = $$L^2/2\mu a$$ ?

Thanks

# Operators commutation and relation between eigenfunctions

If $$H$$ and $$L_i$$ are commuting ( $$[H, L_i] = 0$$ ) could we deduce that the eigenvalues of $$H$$ depend/ do not depend on $$m$$ and $$\ell$$ ( eigenvalue of $$L_z, L^2$$ )? I don't think so since it does not depend for the hydrogen atom but in a more general case could we deduce some relation between eigenvalues when two operators are commuting?

And in the particular case where $$H = L^2/2\mu a$$?

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