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Unformatted text preview: Physics 481: Condensed Matter Physics  Practice Exam Problem 1: Fermi pancakes Consider a thin layer of copper, 1 mm wide and 1 mm long along x and y . The layer is a few ˚ A thick in zdirection. Treat the layer as a free electron gas, demanding the the wavefunction vanishes at the boundaries along the z direction (periodic boundary conditions in x and y directions). The electron density for copper is 8.49 × 10 22 electrons/cm 3 . a) Solve the singleparticle Schr¨ odinger equation for the given geometry and write down the result ing singleparticle wave functions as well as the energy eigenvalues. Specify the values that the quantum numbers can take. b) Find the maximum thickness a of the layer for which only the perpendicular ( z direction) ground state is occupied at zero temperature. c) Calculate the Fermi wavevector in the k x k y plane for this thickness. Problem 2: Hcp extinctions a) The hexagonal Bravais lattice can be defined by the primitive vectors ( a, , 0) , ( a/ 2 ,a...
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This note was uploaded on 10/04/2011 for the course PHYSICS 481 taught by Professor Thomasvojta during the Spring '11 term at Missouri S&T.
 Spring '11
 ThomasVojta
 Physics

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