A photon travels at the speed of light in a vacuum. Your request for "size and shape" really makes no sense. A photon is not really a particle, nor is it strictly a wave. It can behave like a wave in some respects, and like a particle in others. In order to talk about it's shape, you would have to localize it, compress it to a single point. That's not allowed by the Heisenberg Uncertainty principle.
How can you say that something with an FT of 1 (eg. a point) has a specific wavelength, which a photon is supposed to have? Nope, you're going to have to broaden that impulse out in time and decrease the amplitude before anything resembling a dominant wavelength emerges. So, how broad in time is a photon (I can handle multiplying by c all by myself)
If you were to try and localize a photon (treat it as a point) you would be compressing it to an incredibly short light pulse. Such pulses can (sort of) be generated. I used to work in a lab with a femtosecond pulse laser system. A pulse of about 25 femtoseconds (1fs = 10^-13 seconds) is spread out over a distance of less than a millimeter. You are correct that this could not have a single wavelength. It typically has a mix of around 40 nm around a central primary wavelength, as opposed to just a few nm for a standard, continuous laser. Photons are not point-like particles, though they can act like particles in specific circumstances (the photoelectric effect for example).
As an aside, if a unit step em wave hits a stationary point electron, at what distance from the point electron is the reflected wave's electric field equal to and opposite that in the input unit step? What is the significance of the distance? Of course, I'm asking for a classical analysis, if can lower yourself that far.
I think you're describing a photon scattering off an electron here, though I'm not quite certain. The problem is, you're asking for a classical response to a question that ONLY Quantum Mechanics will answer. For one thing, it is IMPOSSIBLE for a photon to scatter off an electron without having the elctron respond. If the photon has a wavelength anywhere near that of the size of an electron, it will also have enough energy to excite and move the electron. For this and other reasons, you NEED QM to solve this problem.
In order to talk about it's shape, you would have to localize it, compress it to a single point. That's not allowed by the Heisenberg Uncertainty principle.
You don't even need to compress it to a point. Just an equation of the overall shape would be fine.
I used to work in a lab with a femtosecond pulse laser system. A pulse of about 25 femtoseconds (1fs = 10^-13 seconds) is spread out over a distance of less than a millimeter.
Cool stuff. What was the application? I've read quite a bit about photoconducting antennas and their applications. Even done a few simulations of it using my TLM program.
I think you're describing a photon scattering off an electron here, though I'm not quite certain. The problem is, you're asking for a classical response to a question that ONLY Quantum Mechanics will answer. For one thing, it is IMPOSSIBLE for a photon to scatter off an electron without having the elctron respond.
Classical em handles scattering fine until you get to extremely short wavelengths. Also, I guess my original scattering post was unclear. It would have been more clear to say an "initially stationary electron". Of course, the electron is free to move in response to the incident wave. My whole point was to show that an incident wave accelerates a point electron in such a way that the scattered wave cancels the incident wave at exactly the classical electron radius. It's weird that this radius can be calculated in several (seemingly) unrelated ways.