We have Schroedinger equation for an electron in a hydrogen atom.

Do we have Schroedinger equation for a photon?

Is it possible for us to imagine a Schroedinger equation for a photon?

We have Schroedinger equation for an electron in a hydrogen atom.

Do we have Schroedinger equation for a photon?

Is it possible for us to imagine a Schroedinger equation for a photon?

I have examined if the usual Schroedinger equation can be used to describe the photon.

Attached a file of simple calculation, please open and have a look.

The big question I encountered in the calculation is the assumption of "virtual photon mass".

Can we justify this assumption and understand its meaning?

According to the recent science polpular books, in the double slits experiment, both of the single electron and the single photon are observed to show the same behavior, that is, the interference pattern at the final screen. Therefore, since the electron obeys the usual time-dependent Schroedinger equation, the unknown Schroedinger equation for photon might resemble the one for an electron. But, because the photon's rest mass is zero, we cannot write the kinetic energy operator term for photon in the equation. How should we proceed?