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# solution_5 - Solutions of Problem set 5 PHYS 361(Solid...

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Solutions of Problem set # 5 PHYS 361 (Solid State Physics), Autumn 2009 1. Thermocouple (a) Using Q = - π 2 k B 2 T 6 F , V = R Q dT = - π 2 k B 2 12 F ( T 2 1 - T 2 0 ), therefore Δ V Δ T = - π 2 k B 2 12 e ( 1 ε F 1 - 1 ε F 2 )( T 0 + T 1 ) = Q 1 ( T ) - Q 2 ( T ), where Δ T = T 1 - T 0 , T = ( T 1 + T 0 ) / 2; (b) ﬁnd the maximal and minimal ε F on the table: ε F Be = 14 . 3 eV, ε F Cs = 1 . 59 eV , then Δ V = 2 × 10 - 6 V when T = ( T 1 + T 0 ) / 2 = 300 K . (c) from Handbook of Chemistry and Physics Δ V Fe - Cn = 1 . 537 × 10 - 3 V, Δ V Cu - Cn = 1 . 196 × 10 - 3 V , using a) you get Q Fe - Q Cu = [( Q Fe - Q Cn T - ( Q Fe - Q Cn T ] / Δ T = (Δ V Fe - Cn - Δ V Cu - Cn ) / Δ T = 1 . 1 × 10 - 5 V/K where T 0 = 270 K and T 1 = 300 K . But from table 2.1 ε F Fe = 11 . 1 eV, ε F Cu = 7 . 0 eV thus Q Fe - Q Cu = 1 . 9 × 10 - 7 V/K , which is 2 order of magnitude oﬀ. 2. reﬂecting and transmitting band structure (a) for the wave coming from left: ψ l ( x ) = ± e iKx + re - iKx , x ≤ -

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solution_5 - Solutions of Problem set 5 PHYS 361(Solid...

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