HW 6 Phys 404 S11

HW 6 Phys 404 S11 - Phys 404 Spring 2011 Homework 6,...

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1 Phys 404 Spring 2011 Homework 6, CHAPTER 4 Due Thursday, March 17, 2010 @ 12:30 PM Chapter 4 assignment: Read chapter 4, then do these problems in chapter 4: 1 . K+K, Chapter 4, Problem 1 2 . K+K, Chapter 4, Problem 2 3 . K+K, Chapter 4, Problem 5 4 . K+K, Chapter 4, Problem 7 Problems in classical statistical mechanics : 5 . A pendulum has length L and mass m, and makes an angle with the vertical direction. Assuming that the amplitude of oscillation is small, find < >, < 2 >, <v>, and <v 2 > when the temperature of the pendulum is . Hint : Express the Hamiltonian in terms of the single coordinate ( ) and conjugate momentum (angular momentum ℓ) of the pendulum. Expand the potential for small oscillations, but take the limits of integration on in the partition function out to ±∞. 6 . Referring to problem 5, what value of mL will give (< 2 > ) 1/2 = 0.001 radian when the pendulum is at T = 300 K? 7 . Consider a classical N-particle system with Hamiltonian given by H = i = 1 N (p xi 2 + p yi 2 + p zi 2 )/2m i + V( r 1 , r 2 , . .. r N ) where V is the potential energy in terms of the coordinates of all the particles. Show that Z can be
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HW 6 Phys 404 S11 - Phys 404 Spring 2011 Homework 6,...

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