Consider Compton scattering of a photon by a moving electron. Before the collision the photon has a wavelength λ and is moving in the positive x direction. The electron is moving in the negative x direction with a total energy E ( including rest energy mc^2). The photon and electron collide head on. After the collision both are moving in the negative x direction.
Derive an expression for the wavelength λ' of the scattered photon. Show that if E>>mc^2, where m is the rest mass of the electron, your result reduces to
The Attempt at a Solution
I've tried many things to manipulate the Compton equation and conservation of energy but I can't seem to get anywhere.