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prob set 5

# prob set 5 - PHYS 271 Problem Set 5 Due Mon Mar 30 2009 at...

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PHYS 271: Problem Set 5 Due Mon., Mar. 30, 2009 at the start of class. 1. Imagine we have a perfect quantum wire attached to two metal contacts. When there is no voltage applied across the wire, each metal has a Fermi energy of 10eV. The wire has a width d . We are interested in the conductance of our wire for very small applied voltages V . (a) What is the smallest value of d for which the conductance of the wire is non-zero? (b) Imagine we ±nd the conductance of our wire to 100 e 2 / h . In this case, what are the possible values of d ? (c) In the limit where d becomes very large, the conductance of the wire will roughly scale as a power of d , i.e. G d l . Find the exponent l . 2. In lecture, we calculated the total transmission probability for an electron to go through two barriers sep- arated by a distance L by summing the amplitude for every possible path the electron could take. For two identical barriers, each having a transmission probability T , we found the result: T total

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prob set 5 - PHYS 271 Problem Set 5 Due Mon Mar 30 2009 at...

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