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Exam2_solutions

# Exam2_solutions - ECE 495W EXAM II 1 page of notes Friday...

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Unformatted text preview: ECE 495W EXAM II 1 page of notes Friday Nov.3, 2006 NAME. PUID # : Please show all work and write your answers clearly. This exam should have ﬁve pages. Problem 1 [p. 2] 8 points Problem 2 [p. 3] 8 points Problem 3 [9. 4,5] 9 points Total 25 points USEFUL RELATIONS: ei 1‘ = cosx + .isinx shim/3) = sin(2n/3) = «E /2 cos(:r/3) = —cos(2n/3) = 1/2 Problem 1: Use the principles of bandstructure to write down the eigenvalues and eigenvectors of the matn‘x (a, b are real numbers) a ib — ib -ib a ib . . ib — ib a 4:44, ' -ﬂmy £3 ﬂ+££¢ -—4; 6/ : a—MW Problem 2: Find the E(kx, ky) relation for an inﬁnite square two—dimensional lattice of side ‘a’ with Hnm = e, if m = n Hnm = 1‘, if m and n are nearest neighbors H ”m = 0, otherwise Problem 3 (9 points) A two-dimensional sheet having an 132(k) relationship E = Bkz, where k2 a (k,2 + [(3,2) , is rolled up along the x~axis to have a circumference ‘0’. Obtain an expression for the density of states D(E). ...
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Exam2_solutions - ECE 495W EXAM II 1 page of notes Friday...

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