Lecture_10

Lecture_10 - PHYS 342 Fall 2010 Lecture Lecture 10...

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PHYS 342 Fall 2010 ecture 10: Lecture 10: Scattering of Matter-Waves Ron Reifenberger irck anotechnology Center Birck Nanotechnology Center Purdue University Lecture 10 1

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Electron Scattering from a Potential Step E Case I: E>V o V(x) m 1 ik x e 1 Be 2 Ce egion 2 V o Ae Region 2 x 2 2 2 2 0 x=0 Region 1 1 1 2 2 2 d E md x mE 2 22 2 2 2 o d VE x mE V  1 2 2 2 1 11 0 k d k    2 2 2 2 2 2 o k d 1 1 2 1 ik ik x x d A Be e x 2 2 2 0 ik x k d e x C 2
) () x Boundary Conditions 00 12 xx dd x dx    x x dx 11 1 ik x ik x xA e B e  2 2 ik x xC e A BC  2 1 1 1 2 k A C k     ik A B ik C  2 1 1 1 2 k B C k  3

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Probability of transmission ver step Probability that incident particle moving to the right is ithin x and +dx <0): over step within x and xdx (x 0) 11 2 1 ** * ik x ik x kk dx v d Ae td t A d t A AA A   m m Probability that incident particle passes over step and within x and +dx >0): is within x and xdx (x>0): 22 2 2 2 * 2 ik x ik x dx v dt dt C dt Ce C e CC  m m Probability of transmission : 2 1 2 4 4 Ck C k k     2 2 2 21 1 2 1 2 1 1 1 1 2 T k k Ak k C k        4
Probability of reflection from step Probability that incident particle moving to the right is within x and x+dx (x<0): 11 2 1 ** * ik x ik x kk dx v d Ae td t A d t m A m AA A  

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Lecture_10 - PHYS 342 Fall 2010 Lecture Lecture 10...

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