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ps2

Course: PHYSICS 601, Fall 2008
School: Rutgers
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Word Count: 172

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601: ~ysics Solid StatePhysicsI fi le:///C:/karin/courses/falI2004/ps2.html This is the first of two problems in PS#2.The second,on crystal structure, will be added on Monday, September 13. Problem 1: The Free and Independent Electron Gas in Two Dimensions (A&amp;Mp. 53) (a) Whatis therelation between andkf in two dimensions? n &quot;c~ (b) What is the relation betweenkf andrs in two dimensions? (c)...

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601: ~ysics Solid StatePhysicsI fi le:///C:/karin/courses/falI2004/ps2.html This is the first of two problems in PS#2.The second,on crystal structure, will be added on Monday, September 13. Problem 1: The Free and Independent Electron Gas in Two Dimensions (A&Mp. 53) (a) Whatis therelation between andkf in two dimensions? n "c~ (b) What is the relation betweenkf andrs in two dimensions? (c) Show that in two dimensions free electrondensityof statesg(e) is a constantindependent e the of for 8>0, and0 for e<O.What is the constant? Show (d) that because g(e) is constant,every term in the Sommerfeld expansion n vanishes for expect the T=Oterm. Deducethat mu=efat anytemperature. (e) Using the relation betweenn, g andmu 00 ?1 = -~ dEj(E;) Ff) ~/kJ T deducethat when g(e) is asin (c), then ./< t k&-rift.. (1-1 e ) ~ ~F (t) Estimatefrom the express...

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