1
Phys 460 Problem Set #3
Fall 2012
Problem 1
(a) For nearly free elections on a 2d square lattice, the kinetic energy of the electrons is
~2 k 2 /2m. The wave number at the corner of the first Brilli
1
Phys 460 Problem Set #5
Fall 2012
Problem 1
In low temperature, the concentration of conduction elections can be approximated as in Eq.
(53) in Kittel:
E
d
1/2 2kB T
n (n0 Nd )
d
(
with n0 2
me kB T
1
Phys 460 Problem Set #3
Fall 2012
Problem 1
(a) For nearly free elections on a 2d square lattice, the kinetic energy of the electrons is
~2 k 2 /2m. The wave number at the corner of the first Brilli
PHY460: Problem Set #2 Due: Friday 10/3 by 5pm in Yellow PHY460 homework box between
Loomis and MRL on 2nd Floor
1. Draw a 5x5 lattice of unit cells for a 2d lattice with Bravais lattice vectors:
(a)
1
Phys 460 Problem Set #2
Fall 2012
Problem 1
(a) (b): If we assume there is one atom in each unit cell, a block of the lattice looks like Fig.
(1).
FIG. 1: Problem 1
(c): (a) has C2 symmetry and (b)
PHY460: Problem Set #1 Due: Thursday 9/13 by 5pm in Yellow PHY460 homework box between
Loomis and MRL on 2nd Floor
Please look over the homework and grading policies in the syllabus before you begin.
1
Phys 460 Problem Set #4
Fall 2012
Problem 1
(a) The solutions for Kronig-Penny model with periodic delta potential satisfy
P
sin Ka + cos Ka = cos Ka,
Ka
(1)
and to nd the energy of the lowest energ
PHY460: Problem Set #1 Due: Friday 9/19 by 5pm in Yellow PHY460 homework box between
Loomis and MRL on 2nd Floor
Please look over the homework and grading policies in the syllabus before you begin.
1.
PHY460: Problem Set #5 Due: Friday 11/21 by 5pm in Yellow PHY460 homework box between
Loomis and MRL on 2nd Floor
1. In a particular semiconductor there are 1019 donors/m3 with an ionization energy (i
PHY460: Problem Set #4 Due: Tuesday 11/4 by 5pm in Yellow PHY460 homework box between
Loomis and MRL on 2nd Floor
1. Consider electrons of mass m in a periodic potential in one dimension given by
X
V
1
Phys 460 Problem Set #1
Fall 2012
Problem 1
(a) Since there is no interaction for the three identical particles, we may set onsite energy as
Ea and shift energy of particles by Ea . Then the hopping
PHY460: Problem Set #6 Due: Friday 12/12 by 5 pm in Yellow PHY460 homework box between
Loomis and MRL on 2nd Floor
1. Monatomic linear lattice: Consider a longitudinal wave
us = u cos(t sKa)
(1)
which
PHY460: Problem Set #3 Due: Friday 10/17 by 5pm in Yellow PHY460 homework box between
Loomis and MRL on 2nd Floor
1. Free electron energies on the square lattice in the empty lattice approximation
(a)
1
Phys 460 Problem Set #7
Fall 2012
Problem 1
(a) The magnetic eld B(x) inside the plate and parallel to it. The penetration equation
2 d2 B/dx2 = B, where is the penetration depth, has the solutions
1
Phys 460 Problem Set #6
Fall 2012
Problem 1
(a) The total energy is composed of the kinetic energy and the potential energy:
X 1
1
2
2
M vs + C(us )
E =
2
2
s
2
N 1
1
1 X dus
1
1X1
2
= M
+ C (u1 u