PHZ 6426 Homework Assignments

M.D. Johnson, Fall 2006

Homework 1 (solution): Marder 1.1, 1.5(a), 2.1, 2.3, 2.6
Homework 2 (solution): Marder 3.1, 3.4, 6.1, 6.2, 6.4, 6.5, 6.8
Homework 3 (solution): Marder 7.2, 7.3, 7.5; and calculate or find the following for Ag at room temperature:

(a) Calculate a heat capacity per unit volume c = 6 x (½ NkB/V) (why 6?)
(b) Calculate a heat capacity per unit volume using Eq. 6.77
(c) Look up the actual heat capacity. Discuss how to understand (a) and (b) given this result.
Homework 4 (solution): Marder 8.1, 8.6; and fill out the multiplication table for the group of the square lattice.
Homework 5 (solution): Marder 10.1, 10.2
Homework 6 (solution): Marder 13.1, 13.2, 13.4; and this:
Atoms of mass M located on sites of a three-dimensional simple cubic lattice are connected to nearest neighbors by ideal springs of spring constant κ.
(a) Calculate the three-by-three matrix &Phi(k);.
(b) Calculate the polarizations and frequencies of the normal modes if wave vector k is in the (100) direction;
(c) Repeat (b) if k is in the direction (1/√3,1/√6,1/√2).
Homework 7 (solution): Marder 13.5; and derive Eq. 13.67 for the Debye model starting from its definition in terms of ωk vs. k.
Homework 8 (solution): Marder 16.1, 16.2 (a) and (c), 16.4
Homework 9 (solution): Marder 17.1, 17.2, 17.4