ps11 - Statistical Physics I(8.044 Spring 2009 Assignment...

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Statistical Physics I (8.044) Spring 2009 Assignment 11 May 6, 2009 Not to be handed in. Readings The reading for Chapter IX of 8.044 is Baierlein Chapters 8 and 9. Problem Set 11, Perhaps Better Called a Study Guide This problem set serves as a study guide for you to build your understanding of the material in Chapter IX of 8.044. This material will be featured on your final exam. But, you will not turn this problem set in. Solutions will be posted late next week. 1. A Number of Two-State Particles Consider a collection of N indistinguishable non-interacting, spinless, Bose particles. There are only two single particle energy eigenstates: φ 0 with energy ε = 0 and φ 1 with energy ε = Δ. (a) How many N -body states are there in all? How would you list them, using the occupation number representation? What are their energies? (b) Evaluate the partition function Z ( N,T ) using the canonical ensemble. [You must evaluate the sum.] (c) What is the probability p ( n ) that n particles will be found in the excited state φ 1 ? Make two plots of p ( n ) for N = 4; in the first plot, take T = Δ /k B and in the second plot take T = 1000Δ /k B . (d) Now suppose that the particles were distinguishable. How many
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ps11 - Statistical Physics I(8.044 Spring 2009 Assignment...

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