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bobred

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## Homework Statement

Is there a state that has definite non-zero values of [itex]E, L^2[/itex] and [itex]L_x[/itex]

## Homework Equations

[itex]L^2[/itex] and [itex]L_z[/itex] commute with the Hamiltonian so we can find eigenfunctions for these

## The Attempt at a Solution

I would say that there is a state with simultaneous eigenfunctions of [itex]L_x,L_y,L_z[/itex] and [itex]L^2[/itex], but with eigenvalues equal to zero. This being the state with [itex]l=0[/itex] and [itex]m=0[/itex], so there are no definite non-zero values of [itex]E, L^2[/itex] and [itex]L_x[/itex]. For other states [itex]L_x,L_y,L_z[/itex] and [itex]L^2[/itex] do not commute.