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Unformatted text preview: Phys 605. Homework 5 Due 5pm, Monday, October 27, 2008 Problem 5-1: [10 pts.] Consider point particles scattering elastically (angle of incidence equals angle of reflection at point of impact) from an infinitely massive, perfectly hard ellipsoid of rotation. The ellipsoid is obtained by rotating the ellipse ( x 2 /a 2 ) + ( y 2 /b 2 ) = 1 about the x axis. The beam of incident particles is directed along the x-axis. (a) Show that the scattered angle is related to the impact parameter s by s = b 2 a b 2 a 2 + tan 2 ( 2 ) - 1 / 2 (b) Find the differential scattering cross-section. (c) What is the total scattering cross-section? Problem 5-2: [10 pts] Prove the following properties of matrices A,B, and C : (a) ( AB ) C = A ( BC ); (b) ( AB ) t = B t A t , where A t is the transpose of A ; (c) The product of two orthogonal matrices is also orthogonal; (d) Tr ( ABC ) = Tr ( CAB ) = Tr ( BCA ); (e) The Tr ( A ) is invariant under any similarity transformation....
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