HW-3 - Theory of Solids HW-3 Solution By Qifeng Shan...

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1 Theory of Solids HW-3 Solution By Qifeng Shan Ashcroft and Mermin’s book 2-3 The classical limit of Fermi-Dirac statistics The Fermi-Dirac distribution reduces to the Maxwell-Boltzmann distribution, provided that the Fermi function (2.56) is much less than unity for every positive ε , for in that case we must have   T k e f B / (2.103) The necessary and sufficient condition for (2.103) to hold for all positive ε is . 1 B /  T k e (2.104) (a) Assuming that (2.104) holds, show that   2 / 1 B 6 / 1 3 / 1 3 / s 2 3 B T mk e r T k (2.105) In conjunction with (2.104) this requires that , 2 2 / 1 B 2 s  T mk r (2.106) which can also be taken as the condition for the validity of classical statistics. (b) What is the significance of the length r s must exceed? (c) Show that (2.106) leads to the numerical condition . K 10 2 / 1 5 0 s  T a r (2.107) (d) Show that the normalization constant m 3 / 4 π 3 ħ 3 appearing in the Fermi-Dirac velocity distribution(2.2) can be written as
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This note was uploaded on 10/04/2011 for the course PHYS 4720 taught by Professor Shan during the Fall '09 term at Rensselaer Polytechnic Institute.

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HW-3 - Theory of Solids HW-3 Solution By Qifeng Shan...

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