731F11_EXAM1 - 1 Rather than starting with a semiclassical...

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Unformatted text preview: 1. Rather than starting with a semiclassical approximation, a quantum mechanical approach to screening in the electron gas would first solve Schroedinger’s equation and then determine the induced charge density from the resulting wavefunction state occupation. a. Write down the wavefunctions resulting from a perturbing potential V( r ) using first- order time-independent perturbation theory. Use your knowledge of the unperturbed wavefunctions to simplify. Your answer will be in terms of an undetermined sum over states. b. Using this first-order wavefunction and the Fermi-Dirac occupation function f(k), determine the real-space charge density δρ ( r ) to first order in V( r ) by summing again over all states. Do not attempt to evaluate either sum (yet). Subtract the unperturbed background. c. Now find the Fourier transform gG ¡ ¢£¤ ¥ ¦gG¢§¤¨ ©ª£u§ « ¬ ­U Note that ¦¨ ª® ¯ ° ¨ ©ª®° «­ ¥ g¢± ² ± ³ ¤U , which enables the evaluation of the sum over one state...
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This note was uploaded on 12/29/2011 for the course PHYSICS 731 taught by Professor Appelbaum during the Fall '11 term at Maryland.

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731F11_EXAM1 - 1 Rather than starting with a semiclassical...

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