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I am trying to understand diffraction on periodic structured in solid state physics.

Q is the source of the spherical wave. R the vector to the object and R+r the vector to the scattering centre P, which gives us a another spherical wave.

All spherical waves are considered as plane waves due to the big distance between P,B and Q.

The magnitude at P can be described as: ##\Psi_P(t) = \Psi_0e^{i(\vec k (\vec R + \vec r)-\omega_0 t)}##

My questions:

1. The magnitude on point Q, which means ##\vec R + \vec r = 0##, is only depending on the time ##t## in ##e^{-i\omega_0 t}##. My book(Ibach, Lueth Festkörperphysik) says that it has a fixed phase anytime. According to wikipedia(https://en.wikipedia.org/wiki/Plane_wave#Complex_exponential_form) the phase ##\varphi## is included in ##\Psi_0##. **What does it mean to have a "fixed phase" especially at location Q?**

2. "You can only use this plane wave approach ##\Psi_B## for *a* emission process." my book says, but why is it so?

3. "In real emitters do atoms send many photons with uncorrelated phases. (Exception: lasers)" my book also says. Does that mean the phase of the different photos are independent to each other?

Q is the source of the spherical wave. R the vector to the object and R+r the vector to the scattering centre P, which gives us a another spherical wave.

All spherical waves are considered as plane waves due to the big distance between P,B and Q.

The magnitude at P can be described as: ##\Psi_P(t) = \Psi_0e^{i(\vec k (\vec R + \vec r)-\omega_0 t)}##

My questions:

1. The magnitude on point Q, which means ##\vec R + \vec r = 0##, is only depending on the time ##t## in ##e^{-i\omega_0 t}##. My book(Ibach, Lueth Festkörperphysik) says that it has a fixed phase anytime. According to wikipedia(https://en.wikipedia.org/wiki/Plane_wave#Complex_exponential_form) the phase ##\varphi## is included in ##\Psi_0##. **What does it mean to have a "fixed phase" especially at location Q?**

2. "You can only use this plane wave approach ##\Psi_B## for *a* emission process." my book says, but why is it so?

3. "In real emitters do atoms send many photons with uncorrelated phases. (Exception: lasers)" my book also says. Does that mean the phase of the different photos are independent to each other?