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Unformatted text preview: states (use the BCS model) is W N ! W S = N(0) " 2 2 (20) 3. Find the transition temperature T c for a three squarewell model with wells K p , K e , and K c having cutoff energies ! 1 , ! 2 , and ! 3 , respectively. Assume K e and K p attractive and K c repulsive with K c < K p < K e . Show that your result reduces to the usual two squarewell model solution when K e = 0. (20) 4. (a) Calculate the BardeenPines interaction (following the discussion given in class) including finite temperatures; that is, put in the phonon occupation numbers. (b) Calculate the electronphonon selfenrgy (with phonon occupation numbers). (c) Estimate N(0) V (Coulomb) and N(0) V (BardeenPines) for a typical metal. (20) 5. For the pair creation and destruction operators, calculate b k ,b " k + [ ] # , b k ,b " k [ ] + , b k ,b " k + [ ] + , b k 2 , and b k + 2 ....
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 Spring '08
 Cohen
 Center Of Mass, Energy, Mass, Momentum

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