Quadrupole operator

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    If I understand well “the equation on the previous slide” means the one for V^(2), where you can see the axial symmetry from the fact V^(2)_{xx} and V^(2)_{yy} are equal.

    From the figure of the toy model it is obvious, since the only effect the dumb-bell can feel is from two charges on a linegoing through the middle of the dumb-bell. This means the two charges of the dumb-bell too always experience the same effect of the two negative charges, so they are in an axial symmetric plane perpendicular to the axis of the two negative charges. On the same distance from the center of the dumb-bell the two negative charges have the same effect in the plane in the center between them perpendicular to the line connecting them. This means there is axial symmetry in this plane.

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