Homework Set # 2 - Due September 11

  
   
1) Problem 1.11

2) Problem 1.13

3) Problem 1.14

4) Problem 2.1

5) Consider the phase space for one single classical particle of mass m in a 1D box of length L. At time t=0 the particle is at the center of the box and has an energy E_0.

a) Draw the point that represents the particle microstate at t=0 in phase space: i) assuming that the particle is moving to the right); ii) assuming that the particle is moving to the left.

b) Consider a volume w with dx=L/10 and and dp=2Δ with Δ<<p_0 around the particle in case [a-(i)]. Draw the volume w in phase space. You can arbitrarily chose the value for p_0 and Δ. What is the volume of w in terms of L and Δ?

c) What will be the position of the point in phase space at t=1s if it was moving to the right? Draw the position of the point assuming that E_0/m=L^2/32.

d) Draw the volume w around the point at time t=1s. Hint: Find the new position of each of the vertices. Assume that Δ/m=L/20. What is the volume of w in terms of L and Δ now?

e) What can you say about the way in which w has evolved?