Discussion8 - what happens for states having E > 0 –...

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Physics 486 Fall 2007 Discussion Problems 8 1) In this problem, as a simple and instructive example, you will explore the tunneling features of the delta function potential. Consider the situation below of an incident particle hitting a delta function from the left and getting partially reflected and partially transmitted. (a) Write down the appropriate time-independent Schrodinger’s equation for this problem. (b) By considering properties of the wavefunction and its derivative at x = 0, express the co-efficients B and C in terms of A, the energy of the particle E, its mass m, the delta function potential strength α , and fundamental constants. (Take care: the delta function makes the derivative of the wavefunction discontinuous.) (c) From the above, find the transmission co-efficient T = |C| 2 /|A| 2 and the reflection co-efficient R = |B| 2 /|A| 2 . What do they add up to? Why? (d) Now revisit the problem in which is α negative (you had previously solved for the bound state wavefunction for E < 0). Based on the above analysis, describe
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Unformatted text preview: what happens for states having E > 0 – strangely, quantum mechanics causes both potential dips and humps to scatter! Physics 486 Fall 2007 2) Two conducting copper wires are separated by a thin insulating barrier made of copper-oxide (CuO). The oxide barrier can be modeled as a square barrier of height V o =10 eV and width L = 1 nm. A 1-mA current of 7 eV electrons in one of the wires is incident on the oxide barrier. (a) Calculate the product κ L for this system. Can you use any approximations for the transmission coefficient T? (b) Use the exact expression for the transmission coefficient to determine the probability that an electron will tunnel through the oxide barrier. (c) Given that there is a current of 1-mA in one of the wires, about how many electrons should tunnel through the barrier per second? (d) How much current will tunnel through to the adjacent wire? What happens to the remaining current?...
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This note was uploaded on 09/20/2010 for the course PHYS 486 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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Discussion8 - what happens for states having E > 0 –...

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