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Unformatted text preview: 1 Theory of Solids HW-1 Solution By Qifeng Shan Ashcroft and Mermin’s book 1-1 Poisson distribution. In the Drude model the probability of an electron suffering a collision in any infinitesimal interval d t is just d t / τ . (a).Show that an electron picked at random at a given moment had no collision during the preceding t seconds with probability e t / τ . Show that it will have no collision during the next t seconds with the same probability. (b).Show that the probability that the time interval between successive collisions of an electron falls in the range between t and t + d t is (d t / τ ) e t / τ . (c). Show as a consequence of a) that at any moment the mean time back to the last collision (or up to the next collision) averaged over all electrons is τ . (d). Show as a consequence of b) that the mean time between successive collisions of an electron is τ . (e).Part (c) implies that at any moment the time T between the last and the next collision averaged over all electrons is 2...
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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.
- Fall '09
- Solid State Physics