homework5

homework5 - Homework#5 — PHYS 603 — Spring 2008...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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, μ H < D and μ 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 ² n = ¯ hω ( 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 ( β ) of N classical harmonic oscillators using the formula Z ( β ) = Z ∞ Ω( E ) e- βE dE, (1) where E is the total energy of N oscillators, and Ω( 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....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

homework5 - Homework#5 — PHYS 603 — Spring 2008...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online