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Unformatted text preview: since G has to be zero ( no wave coming back from large x) In region II ( 0 < x < L ) where U = U (non-zero and assumed to be greater than E) II = Ce " x + De # x where 2 = 2 m h 2 ( U " E ) (b) Wavefunction and its derivative continuous at x=o gives A + B = C + D (1) ikA ! ikB = " C ! D (2) Same conditions at x=L gives Ce ! L + De " L = Fe ikL (3) Ce L " De " L = ikFe ikL (4) (c) We are given that L >> 1, so we can set e ! L to zero in above equations Then the only way (3) and (4) can be simultaneously satisfied is if C = F = 0. Then Eqs. (1) and (2) become: A + B = D A B = (i /k)D Solution gives B A = k ! i k + i so R = B A 2 = 1...
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This note was uploaded on 12/07/2009 for the course PHYS phys 2d taught by Professor Hirsch during the Spring '08 term at UCSD.
- Spring '08