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ME501HW2SolnF2011

ME501HW2SolnF2011 - 1 ME 501 Homework#2 Due Monday October...

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1 ME 501 Homework #2 Due Monday, October 3, 2011 Prof. Lucht (E-mail address: [email protected]) 1. NML, problem 3.5, p. 148. 2 2 2 . ( ) - 2 : , 0, Free particle of mass m moving on circle of radius a a Schrodinger equation r V r r steady state SWE m For free particle V r t r a operator in cylindrical coord    : 1 inates r r r r 0 2 2 2 2 2 1 r z 0 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 0 2 2 ( ) 2 0 2 A 0 in in in Hence But I ma m a d so I d b Solution to Schrodinger equation d I Ae d Substitution gives I n e Ae      2 2 2 * 0 2 2 1 2 2 Normalization gives d =1 e e d =1 1 So 2 1 2 Therefore the normalized solution becomes 2 e = 2I / in in in I n A A A n   
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