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Unformatted text preview: 1 C:\User\Teaching\505-506\S11\HW06'sol.doc PHY 506 Classical Electrodynamics II Spring 2011 Homework 6 with solutions Problem 6.1 (10 points). Photon with wavelength is scattered by an electron, initially at rest. Considering the photon as an ultrarelativistic particle (with the rest mass m = 0), find wavelength of the scattered photon as a function of the scattering angle (see Fig. below). Solution : This the famous Compton scattering problem. It may be most simply solved by writing the laws of conservation of the total energy and momentum, in the lab reference frame: 2 / 1 2 2 2 2 2 c p c m ' c m e e , , p k k ' where p is the momentum of the electron after the collision (see Fig. above), and k = / c = 2 / . From the last equation, we can write cos ' 2 ' ) ( 2 2 2 2 2 2 kk k k ' p k k . (Notice that this is a useful way to avoid the introduction of the direction of vector p .) Plugging this expression into the first equation, and solving for...
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