Depiction of distribution of photons over time

[entropy1]

I have a question about photons and the Schrödinger equation.

Photons behave like particles but also as waves. I understand that this can be described by the Schrödinger equation as a photon having a certain probability to be somewhere.

If I understand this correctly, I take it that there are places in which the photon is more likely to be found than other places. Since a photon travels, the following question arose with me: how does the spatial distribution of the probability of the photon being somewhere evolve over time? Is this what the Schrödinger equation describes? Is there an easy (layman) way to depict such a distribution? (over time)

Thanks.

 

[andrewkirk]

I understand that this can be described by the Schrödinger equation as a photon having a certain probability to be somewhere.
...
Is this what the Schrödinger equation describes? Is there an easy (layman) way to depict such a distribution? (over time)

The second part is correct, but not the first. The Schrodinger equation describes the evolution of a quantum system's state over time. But it cannot on its own tell you anything about the probability of a photon observation occurring at a particular place. For that, initial conditions are needed, such as the wave function at time t=0.

 

[entropy1]

For that, initial conditions are needed, such as the wave function at time t=0.

That is exactly what I mean. If this is given, is there an easy way to visualize the spatial probability distribution evolution?

I imagine a wave-like distribution of which the amplitude differs over space and evolves over time.

 

[jtbell]

The Schrödinger equation is part of non-relativistic quantum mechanics. Photons are quintessentially relativistic quantum objects. You have to use quantum electrodynamics (a quantum field theory) to describe them. Photons don't even have a wave function in the sense of the $\Psi$ of the Schrödinger equation. See the following previous discussion for example:

https://www.physicsforums.com/threads/about-wave-function-of-photon.791842/