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Unformatted text preview: Homework #5 PHYS 603 Spring 2008 Deadline: Thursday, March 27, 2008, in class Professor Victor Yakovenko Office: 2115 Physics Web page: http://www2.physics.umd.edu/yakovenk/teaching/ Textbook: Silvio Salinas, Introduction to Statistical Physics Springer, 2001, ISBN 0-387-95119-9 Do not forget to write your name and the homework number! Each problem is worth 10 points. Ch. 5 Canonical Ensemble 1. Problem 5.1, Spin chain with energy S 2 j in a magnetic field. Do all parts of this problem for a non-zero magnetic field H 6 = 0! Consider two cases, H < D and H > D . Make sure that your answers in this Problem agree with your answers in Problem 4.1 of Homework 4 in the limit H 0. 2. Problem 5.4, Harmonic oscillators with odd n . The energy spectrum discussed in this Problem would arise when the oscillators are restricted by an impenetrable barrier at x = 0, so that x > 0 for each oscillator. In this case, the quantum mechanics demands that the wave functions must vanish at x = 0. This condition is consistent only with the antisymmetric wave functions of the oscillator. Thus, the permitted quantum numbers are the odd numbers n = 1 , 3 , 5 ,... with the energies n = h ( n + 1 / 2), where n = 0 corresponds to the ground state. 3. Problem 5.6, Partition function for N classical harmonic oscillators. 4. Modified Problem 5.7, Partition function for N classical harmonic oscilla- tors from canonical perspective. Calculate the partition function Z ( ) of N classical harmonic oscillators using the formula Z ( ) = Z ( E ) e- E dE, (1) where E is the total energy of N oscillators, and ( E ) is the density of states calculated in Problem 2.5. Find the maximum of the integrand in Eq. (1) and integrate in a smallin Problem 2....
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