Homework Assignments for Physics 603, Spring 2013
Problem Set #1 (2/5: fixed "typo" in 2b: M -> m)
Problem Set #2 (2/14: more explicit wording in 4c in response to a comment after class)
Problem Set #3 (Warning: do the "problem 4" on p. 1, not the qualifier problem on p. 2!
Hint added after office hours: on problem 2d, note that at low temperature, θ will be limited to small values by the exponential term in the integrand, so that the finite limits on the relevant integrals can be extended to ± ∞, to excellent approximation.)
Problem Set #6 The due date and dateline have been pushed back one lecture. Another problem is added, with lots of hints, and the qualifier problem is now included.--A student inquiry indicates confusion about the hint in problem 2 (PB 7.25). The idea is to write the difference in heat capacities in terms of an integral over ω of the density of states (in the Debye model) times the difference between associated ω-dependent energy densities (the classical ω-independent equipartition result and the Planck formula); then use the original hint.
Problem Set #7 The numbers in problem 3 are problems at the end of chapter 8 of PB; the assignment has been updated to say so explicitly.
Regarding problem 5, note that you already did the first 3 parts in Set #3. You should only submit parts d, e, f.!
Here are some hints/milestones for PB 8.1, developed after interactions with a few inquiring students:
To avoid careless mistakes I used Mathematica to check expansions and integrals. Let me write t for kBT/εF. Then the consistency condition for N becomes
N = (1/10) N t3/2 [(ξ +2)5/2 - [(ξ-2)5/2]
leading to
tξ = [1 - 1/(2ξ2)]-2/3 or about ξ = (1/t)[1 – (1/3) t2 + …]
Similarly, U = (3/70) N εF t5/2 [(ξ+2)7/2 - [(ξ-2)7/2]