Photon with spin 1. But it only has two projection along z. Why?

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SUMMARY

The discussion centers on the nature of photons, specifically why they exhibit only two polarization states along the z-direction. According to Shankar's "Principles of Quantum Mechanics," photons must satisfy the transverse condition, which dictates that their wave function components along the direction of propagation (z-direction) must be zero. This leads to the conclusion that the spin projection Sz=0 does not exist for photons, as their polarization is confined to the plane perpendicular to their direction of travel.

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xfshi2000
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Hi all:
I am confused about why photon only has two projection along the z-direction. This confusion came from what I read in shankar "printciple of quantum mechanics". In the chapter of field quantization, he explain that because photon must satisfy transverse condition. wave function component along propagation direction is zero. if it is non-zero, it must be remains invariant under rotation (Jz). that is to say, Sz=0 projection is not existed. I don't understand these words meaning. How did he get this conclusion? thanks.
xfshi
 
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Think of it in terms of polarization. The polarization of the EM wave is in the plane perpendicular to the direction of propagation. Therefore, there is no polarization component along the direction of propagation. For a photon, the latter would corresponds to ##S_z = 0##.
 

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