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The solution is that the Lagrangian is unchanged by a rotation of dΦ together with a translation of hdφ/(2π) (about and along the symmetry axis) where h is the pitch of the helix. This implies that M

_{z}+hP

_{z}/(2π) is conserved where M and P are the angular and linear momenta and _z means the component along the symmetry axis.

It’s a very nice example of Noether’s theorem, but I have one question:

Is he silently assuming that the helix is right handed? Surely for a left handed helix the conservation law would be M

_{z}-hP

_{z}/(2π), right?

Just want to make sure I’m understanding that correctly because Landau never mentions the orientation of the helix, but I think it matters.

Thanks.