For an atom, the single photon electric dipole selection rules for the magnetic quantum number require that delta_m = -1, 0 or +1.(adsbygoogle = window.adsbygoogle || []).push({});

As I understand, the physical explanation for this set of selection rules is usually related to the conservation of the projection of the angular momentum on the quantization axis.

This leads to delta_m = + or – 1 for right or left circularly polarized light and delta_m=0 for linearly polarized light.

My question then is, what exactly do we mean by the quantization axis? Does it need to be the direction of photon propagation? On one hand, it seems that it should be, since the projection of the spin angular momentum of a photon is either +1 or -1 on the direction of propagation (also defined as its helicity). But on the other, we also know that a photon cannot have zero angular momentum in its direction of propagation.

On a related note, if we think of a linearly polarized photon as having equal probability of being left and right circularly polarized, why isn’t delta_m = + or -1 allowed for linearly polarized light?

Can someone point out the errors in my argument? Thanks!

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# Photon angular momentum and magnetic quantum number selection rules

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