Homework Set # 5 - Due September 27

1. Consider a system that can be in any of the following 5 states: 0, +, -, ++, and - - with energies E(0)=0, E(+)=E(-)=ε, E(++)=E(- -)=2ε. If the energy E of the system is such that ε-δ<E<ε+δ, (with δ<<ε), find the probabilities P(0), P(+), P(-), P(++) and P(- -)

   a) in the microcanonical ensemble;

   b) in the canonical ensemble.

   In both cases plot the probability P(ε) vs ε. Hint: you need to provide the actual numerical value of each probability and check that they are normalized as expected.

2. Problem 3.20

3. Problem 3.21 (do only part (a) in the classical case).

4. Problem 3.22 (Hint: Use that the integral over x from – to + infinitity of exp(-ax^4) is proportional to (a)^{-1/4}).

5. Problem 3.42