# HW9 - University of Colorado Department of Physics PHYS3220...

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Unformatted text preview: University of Colorado, Department of Physics PHYS3220, Fall 09, HW#9 due Wed, Oct 22, 2PM at start of class 1. Potential barrier (Total: 20 pts) For the potential with a barrier of height V V ( x ) = , x < V < x < a , a < x the transmission coefficient for 0 < E < V is given by T = 4 κ 2 k 2 ( k 2 + κ 2 ) 2 sinh 2 ( κa ) + 4 κ 2 k 2 . (Note: It is not part of the problem to derive this formula using the boundary conditions discussed in class. But, you may want to check it.) a) Demonstrate that this expression can be rewritten as: T- 1 = 1 + 1 4( E/V )(1- E/V ) sinh 2 ‡ a ~ p 2 m ( V- E ) · b) Consider an electron approaching the barrier. Its initial energy is 0.5 eV and the barrier height is 1 eV, while the width of the barrier is 5 × 10- 10 m. What is the numerical probability for the particle to make it to the other side of the barrier? (Hint: You can (but do not have to) study this tunneling problem by going to phet.colorado.edu and running the ”Quantum Tunneling and Wave Packets” sim.phet....
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HW9 - University of Colorado Department of Physics PHYS3220...

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