When a photon and an electron collide, their interaction can be described using quantum electrodynamics (QED), which is the quantum field theory that combines quantum mechanics with electromagnetism.
In the context of quantum mechanics, particles are described by wave functions, which are mathematical representations that contain information about the probabilities of different outcomes when the particles are measured. When a photon and an electron interact, their wave functions combine, resulting in an entangled state.
The interaction between the photon and the electron is typically described as a scattering process, where the properties of the particles, such as their momentum and energy, can change. The specific details of the interaction depend on the nature of the collision, including the energy and angle of incidence of the incoming photon.
Regarding the collapse of the wave function, it is important to note that the collapse occurs when a measurement is made on a quantum system. In the case of the photon and electron collision, if a measurement is performed on one of the particles, such as detecting the position or momentum of the electron, the wave function describing that particle will collapse to a particular state corresponding to the measurement outcome.
However, it's worth mentioning that the interaction between the photon and electron does not necessarily require the collapse of their wave functions. The collapse of the wave function typically occurs when a quantum system interacts with a macroscopic measurement apparatus or when an observer makes a measurement.
In the case of the photon and electron collision, they can act as mutual observers to some extent, affecting each other's wave functions through their interaction. However, the collapse of the wave functions is usually associated with the measurement process performed by an external observer rather than by the particles themselves.
Overall, the precise behavior of the wave functions of the photon and electron during their collision depends on the specific experimental setup and the interactions involved. Describing these interactions accurately requires the formalism of quantum field theory, such as QED, which provides a framework to understand and calculate the probabilities and outcomes of particle interactions.