class33 - Todays class: Quantum tunneling Review: The...

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Today’s class: Quantum tunneling 4.7 eV y x III Be x α ψ = ) ( Inside well (E>V): (Region II) ) ( ) ( 2 2 2 x k dx x d II II = ) ( ) ( 2 2 2 x dx x d III III = Outside well (E<V): (Region III) ) cos( ) sin( ) ( kx D kx C x II + = Outside well (E<V): (Region I) Review: The finite square well V=0 eV 0 L Energy x E electron 1) ψ(x) has to be continuous: 2) ψ(x) has to be smooth: 3) ψ(|x| ) 0 (required for normalization) ) ( ) ( L L III II = ) ( ' ) ( ' L L III II = 0 L E electron Review: ‘Penetration depth’ 2 m E<V: Classically forbidden region ) ( 2 E V = h ) ( ) ( L x Be x = , with ) ( L e L / ) ( 1/ α Penetration depth: Distance 1/ α over which the wave function decays to 1/e of its initial value at the potential boundary (here (L) ): For V-E = 4 eV, 1/ α ~ 0.1 nm (very small ~ an atom!!!) x ψ 0 L x Be x = ) ( ) ( 2 2 E V m = h What changes would increase how far the wave with: Q1 penetrates into the classically forbidden region? A. Decrease potential depth (= work-function of metal) B. Increase potential depth C. Decrease wire length L D. Increase wire length L E. More than one of the above Wide vs. narrow finite potential well
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This note was uploaded on 08/24/2010 for the course PHYS 2130 taught by Professor Staff during the Spring '08 term at Colorado.

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class33 - Todays class: Quantum tunneling Review: The...

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