Wave function with a certain wavelength

[bubblewrap]

I have a number of questions about the wave function -
1. Do photons have wave functions like the one in Schrödinger equation?
2. If they do, when you send out a wave function with a certain wavelength, then because you know the momentum with no uncertainty the uncertainty of the position becomes infinite and you don't know where the photon is. What happens then? For example if you send out that wave to experiment the photoelectric effect, when the light(photon) hits the particle then the particle 'knows' where the photon is and therefore its uncertainty in the position becomes very small, and as a consequence the uncertainty in the momentum becomes very large; does this mean that the light will suddenly have various wavelengths?

My guess for question 2 is that you can't send out a light of definite wavelength.

 

[Orodruin]

Any wave packet will contain several wavelengths unless it is infinitely extended. This is true for all waves. However, note that $\hbar$ is very small. You can have a wave with a very small uncertainty in wavelength even if your uncertainty in position is of the order of magnitude you would expect from the photoelectric effect.

Also, photons definitely do not follow the Schrödinger equation. The Schrödinger equation describes a non-relativistic massive particle, which the photon most certainly is not. It is about as far away from it as you can get.