Physics 463
Winter 2012
HW # 02 Solutions
1. The Wigner-Seitz cell is a special kind of primitive cell where the lattice point is in the center of the cell.
Each point in the boundary is the minimum lies equidistant between one or more other lattice point
Physics 463
Winter 2012
HW #01 Solutions
1. Discuss qualitatively the various mechanisms of bonding. Give examples of materials for each type of
bond and also materials that do not have a clear single bond type.
Read chapter 3 to nd out the solutions.
Mol
Physics 463
Winter 2011
HW # 07 Solutions
1. a. The donor ionization energy is given by Equation 8.51, which is an analogy to the hydrogen atom taken into
account a dierent eective mass and dielectric screening:
13.6 me
2m
Ed =
eV in CGS units
Ed = 6.296
Physics 463, W12
Name (First, Last): _
VI. Energy Bands in Solids (due Mar. 29)
Reading: Kittels Chap 7, 8 (1st half) & 9: p161-204, p221-235, 242-255.
Ashcroft & Mermin Chap 8-10 & 12.
A function () has the same periodicity of a Bravais lattice. Prove th
Physics 463
Winter 2012
HW # 06 Solutions
1. Show V (r) =
G
VG eiGR where G are the reciprocal lattice vectors.
V (r) = V (r + T) =
G
VG eiGR eiGT
Therefore eGT = 1 for this to be satised. If G is a reciprocal lattice vector, then eiGT = ei vj ni ai bj =
Physics 463, W12
Name (First, Last): _
V. Free Electron Gas Theory of Metals (due Mar. 8)
Reading: Kittels Chap 6, Ashcroft & Mermin Chap 1-3.
1. Particle in the box: Quantum well lasers. (10 pts)
Confinement of electrons in a quantum well leads to standi
Physics 463
Winter 2012
HW # 05 Solutions
1. A quantum well refers to connement of the electrons wavefunction in one direction and in the simplest case,
an innite square well (see Figure 6.2). The energy of the nth level is given by Equation 6.3
222
En =
Physics 463
Winter 2012
HW # 04 Solutions
1. a. The problem assumes that the restoring force is due to the uniform sea of electrons inside the sphere of
en r )
radius r. The electric eld from such a sea of electrons is 0(r2 where n(r) is the number of ele
Physics 463
Winter 2011
HW # 03 Solutions
1. a. The Miller indices, (hlk ), dene a plane that intersects the points a1 , al2 and a3 where ai are the primitive
h
k
vectors of the space lattice.
Therefore, the lines l1 = a1 al2 and l2 = a1 a3 lie in the pla
Physics 463, W12
Name (First, Last): _
II. Crystal Structure (due Jan. 26)
Reading: Kittels Chap 1 (p1-23), Ashcroft & Mermin Chap 4 (& Chap 7).
1. 2D Wigner-Seitz Cells (20 pts)
Please draw the Wigner-Seitz Cells for all 5 of the 2D Bravais lattices, and
Physics 463, W12
Name (First, Last): _
I. Crytal Binding (due Jan. 17)
Reading (invaluable): Kittels, p49-73; Ashcroft & Mermin, p373-414.
Further study and references:
i. Anderson, P.W. More is Different. Science 177, 393-396 (1972).
ii. Pauling, L. The