p605hw6f08wsoln

p605hw6f08wsoln - Phys 605 Homework 5 Due 5pm Monday...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 Θ is related to the impact parameter s by s = b 2 a • b 2 a 2 + tan 2 ( Θ 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....
View Full Document

{[ snackBarMessage ]}

Page1 / 8

p605hw6f08wsoln - Phys 605 Homework 5 Due 5pm Monday...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online