From the previous post "\(\psi_{max}\) Is New And Important",
\(F=\psi_{n}-\psi_o=m\cfrac{dv}{dt}\)
assumes that the photon \((\psi_{n}-\psi_o\)) is absorbed by the particle instantaneously. This may not be true. In this case, the transit particle gain non zero momentum at \(\psi(x=x_a/2)=\psi_{max}\), as it was accelerated. It is then decelerated beyond \((x_a/2,\,\psi_{max})\). The particle will oscillate about \((x_a/2,\,\psi_{max})\), until it emits the packet of energy gained and make a downward energy transition.
Is the photon absorbed by the particle instantaneous, on direct collision, or is the transfer of energy from a passing photon in helical motion to the particle gradual?