852_2010hw11 - PHYS852 Quantum Mechanics II, Spring 2010...

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Unformatted text preview: PHYS852 Quantum Mechanics II, Spring 2010 HOMEWORK ASSIGNMENT 11 Topics covered: Scattering amplitude, differential cross-section, scattering probabilities. 1. Using only the definition, G = ( E H + i ) 1 , show that the free-space Greens function is the solution to bracketleftbigg E + planckover2pi1 2 2 M 2 vector r bracketrightbigg G ( vector r,vector r ) = 3 ( vector r vector r ) . (1) The purpose of this problem is just to establish the equivalence between our operator-based approach, and the standard Greens function formalism encountered, e.g., in classical EM. 2. If we define the operator F via f ( vector k , vector k ) = ( vector k | F | vector k ) , then it follows that F = (2 ) 2 M planckover2pi1 2 T , where T is the T-matrix operator. In principle, one would like to deduce the form of the potential V from scattering data. First, derive an expression for the operator V in terms of the operators G and T only....
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This note was uploaded on 12/21/2011 for the course PHYS 852 taught by Professor Moore during the Spring '11 term at Michigan State University.

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852_2010hw11 - PHYS852 Quantum Mechanics II, Spring 2010...

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