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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 z-direction. 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 single-particle Schr¨ odinger equation for the given geometry and write down the result- ing single-particle 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