Sure. The response is that you are still deliberately lying about my treatment. It does not use or depend on the wave at all.

My analysis has been simply conservation of momentum. Invoking the wave directions does not absolve you from the responsibility of balancing the initial momentum with the momentum of the final state.

You have a photon with momentum in a certain direction. That momentum must be conserved, and it is not conserved in your reaction. You can do an energy momentum budget just by adding up the energy and momentum of all the particles involved in the reaction.

I take it back. High school students can do energy momentum budgets; but we have yet to see a complete balanced budget from Lyndon, that takes both energy and momentum into account and shows them conserved.

But let's talk about waves, if you prefer that approach. This gives another proof that the photo-absorption by an electron is impossible.

The wave is longitudinal. It therefore gives the electron a push to one side. Therefore the photon cannot be absorbed, since it must go off to the opposite side to counterbalance. Equal and opposite reactions -- but violated if the photon is absorbed. Therefore absorption is impossible.

If you EVER get around to doing a complete energy momentum budget, you will have to consider that the electron DOES get pushed sideways, and you have to find SOMETHING ELSE pushed the other way to balance.

In real physics of photoabsorption, it is the positive nucleus.

In real physics of Compton effect, it is a scattered photon.

In the Lyndon effect, there is nothing to compensate the sideways movement of the electron, and so the effect is a violation of trivial school level physics.

Cheers -- Sylas