Advanced Solid State Devices
AUC ECNG 5210
Tarek K. Ghanem
Lecture 3
Introduction to QM
1-D examples: The periodic potential
For a general periodic potential
V(l+x) = V(x) , it can be proven that
any solution to Schrdingers
equation must have the form:
(
Advanced Solid State Devices
AUC ECNG 5210
Tarek K. Ghanem
Lecture 1
Course contents
Introductory atomic and quantum physics
Energy bands and charge carriers in solids, semiconductors
Carrier concentrations in equilibrium, Fermi levels
Nonequilibrium carr
Advanced Solid State Devices
AUC ECNG 5210
Tarek K. Ghanem
Lecture 4
Crystalline structure
Directions in a lattice
A direction in a lattice is expressed as the ratio of the three unit vectors
a1, a2 and a3, and is given as [uvw] where u,v,and w are all in
Advanced Solid State Devices
AUC ECNG 5210
Tarek K. Ghanem
Lecture 2
Introduction to QM
Boundary conditions
(r ) 0,
as
r
Except for free particles
(r )
Is always continuous
(r )
Is always continuous, except at the
boundary with an infinite potential
Sc
ECNG 5210
HW1: Introduction to quantum mechanics
Due 2-10-2015
1- What are the units of the wave function ? (Notice the dependence on dimensionality).
2- A particle of mass m has the wave function ( x ) = Ae ax , where A, and a are positive real
constants
ECNG 5210
HW2: Introduction to quantum mechanics
Due 2-17-2013
1- (This is a qualitative problem, no calculations are required) Consider the 1-D potential shown in
Fig. 1-a below:
(a) Which of the three energy states shown is free, and which is bound? Ske
ECNG 5210
HW4: Crystalline structure, the free electron gas
Due 3-3-2015
1- The face-centered cubic is the most dense and the simple cubic is the least dense of the
three cubic Bravais lattices. The diamond structure is less dense than any of these.
(a) O
ECNG 5210
HW3: The periodic potential, crystalline structure
Due 2-24-2015
1- Imagine a bead of mass m that slides frictionlessly around a circular wire ring of circumference a.
(This is just like a free particle, except that ( x) = ( x + a) ). Find the s