Physics 241 Reading
-----------------------------------------------------------------------------------------------------------
Homework #1 (due Wednesday, September 17,
in class): Ashcroft & Mermin,
Chapter 4, problems 1 [3 points], 3 and 5 [2 points]. Please remember to
staple your sheets together to ensure that they don't get separated or lost in
the grading process. Thank you. As we are posting the solution sets
(with the goal of posting them on the day the homework is due) we cannot accept
late assignments.
[Hints: 4. 1(b) consider the basis
which includes one point in a corner of the cube and two of its nearest
neighbors; 4.1(c) consider the basis which includes one point in a corner of
the cube and three of its nearest neighbors; 4.5(b) in order to calculate the
density of the hcp structure one has to find the
volume of a unit cell and the number of atoms per unit cell. A convenient
choice of the unit cell is the following: consider 1 atom and 6 atoms around it
in the lowest layer + 3 atoms in the second layer on top of those + 7 atoms in
the third layer right above the 7 atoms in the lowest layer. Remember that one
atom can belong to several unit cells! ]
-----------------------------------------------------------------------------------------------------------
Reading #2: Read the text
“Quasicrystals” distributed in class,
Ashcroft & Mermin, Chapter 1, “The Drude Theory of Metals”, and Chapter
2, “The Sommerfeld Theory of Metals”.
Look through Chapter 3, “Failures of the Free Electron Model”. Finish
the reading by Friday, September 26.
Homework #2 (due Wednesday, September 24,
in class): Ashcroft & Mermin,
Chapter 4, problem 6 [4 points]; Chapter
5, problems 1 [3 points] and 2(a); Chapter 6, problem 5(a).
-----------------------------------------------------------------------------------------------------------
Homework #3 (due Wednesday, October 1, in
class): Ashcroft & Mermin, Chapter
1, problems 1 [3 points], 2 and 3;
Chapter 2, problem 1(a,b,c); and the following
problems:
Problem 1. Consider an ideal metal in the Drude
model, i.e. assume that 
.
Calculate the ac conductivity at the frequency 
.
Problem 2. (a) Calculate the
energy of the free non-interacting electron gas at zero temperature. The number
of electrons is N, the Fermi energy is 
. (b)
Find the pressure of the free non-interacting electron gas at zero temperature.
The energy of the gas is E and the volume is V.
Problem 3. The atom 
has spin 1/2. The density of liquid is 0.081 
near absolute zero. Calculate the Fermi energy
and Fermi temperature.
-----------------------------------------------------------------------------------------------------------
Homework #4 (due Friday, October 10, in
class): Ashcroft & Mermin, Chapter
8, problems 1 (all subproblems except (h)) [4 points]
and 2 [3 points];
-----------------------------------------------------------------------------------------------------------
Homework #5 (due Monday, October 20, in class): Ashcroft & Mermin, Chapter 9, problems 1 [2 points], 3(a) and 5(a) [2 points]. These are important problems about a key topic: band theory.
-----------------------------------------------------------------------------------------------------------
Reading #6: Read Ashcroft
& Mermin, Chapter 22, “Classical Theory
of the Harmonic Crystal” (pages
422-443), Chapter 23, “Quantum Theory of the
Harmonic Crystal”, and Chapter 24, “Measuring Phonon
Dispersion Relations” (pages 470-474). Look
through Chapter 21, “Failures of the Static Lattice Model”. Finish the reading by Friday, November 7.
Homework #6 (due Wednesday, October 29, in
class): Ashcroft & Mermin, Chapter
12, problems 1, 3
[2 points] and 4(a); Chapter 14, problems 1 and 2; Chapter 17, problem 3; and
the following problem:
Quantum wire forms a square box of width a. Electron
states form subbands characterized by the integer
indexes 
and 
.
Find the linear electron density at which the = =2 subband
is first populated at equilibrium at T=0. Assume an infinite confining potential at the wire boundary.
-----------------------------------------------------------------------------------------------------------
Homework #7 (due Wednesday, November 12,
in class): Ashcroft & Mermin,
Chapter 19, problem 2 [2 points]; Chapter 22, problems 1, [4 points] and 2 [3 points]; Chapter 23,
problem 2(a,b); Chapter 24, problem 1 [2 points].
-----------------------------------------------------------------------------------------------------------
Homework #8 (due Monday, November 24, in
class): Ashcroft & Mermin, Chapter
28, problems 2(a), 3, 4 (a,b)
[2 points] and 7.
-----------------------------------------------------------------------------------------------------------
Homework #9 (due Wednesday, December 10,
in class): Ashcroft & Mermin,
Chapter 31, problem 8;
Chapter 34, problem 1 [3 points] and the following problem:
Calculate the magnetization of the system of N weakly
interacting Ising spins with the magnetic moment 
in the magnetic
field H at the temperature T. [Hint:
weak interaction can be neglected]
Hints to problem 34.1: (a) the Gibbs free energy is the same in both
phases on the phase transition line; (b)
; (c) express the specific heat via the derivative of the
entropy, dS/dT.
-----------------------------------------------------------------------------------------------------------