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

• xfshi2000
In summary, the confusion about why photons only have two projections along the z-direction is due to the transverse condition they must satisfy, as explained in Shankar's "Principle of Quantum Mechanics." This means that the wave function component along the direction of propagation is zero, and any non-zero component must remain invariant under rotation (Jz). This also means that the Sz=0 projection does not exist, as it corresponds to the polarization component along the direction of propagation, which is zero for photons.
xfshi2000
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

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##.

## 1. What is a photon with spin 1?

A photon with spin 1 refers to a type of subatomic particle that carries energy and has a spin quantum number of 1, indicating its intrinsic angular momentum.

## 2. Why does a photon with spin 1 only have two projections along the z-axis?

This is because the spin of a particle can only be measured along one axis at a time, and a photon with spin 1 has two possible spin states: +1 and -1 along the z-axis.

## 3. How does the spin of a photon affect its behavior?

The spin of a photon does not directly affect its behavior, but it does play a role in determining the polarization of the photon, which can affect how it interacts with other particles.

## 4. Can a photon with spin 1 have a spin projection of 0 along the z-axis?

No, a photon with spin 1 can only have spin projections of +1 or -1 along the z-axis. This is because a spin projection of 0 would require the photon to have a spin quantum number of 0, which is not possible for a photon.

## 5. What other properties does a photon with spin 1 have?

In addition to its spin, a photon with spin 1 also has properties such as energy, wavelength, and frequency, which are all related to its electromagnetic nature.

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