Quantum Mechanics - exercise sheet 2 solutions
Nicolas Poilvert
September 26 2007
In order to nd the quantum mechanical expression for a physical observable
that has a classical analog, we use the anonical quantization rules. Those
rules state that if a c
Homework
Nicolas Poilvert
8
Nicola Marzari
November 6, 2007
1
Propagation equation in a non dispersive medium.
Consider the following propagation equation in an innite, one-dimension medium:
@2y
@x2
1 @2y
=0
v 2 @t2
where y is a real function and v is cal
Homework
5, solution
Nicolas Poilvert
Nicola Marzari
October 22, 2007
Homework is due on Wednesday October 17th, 5pm
1
Density of states
We saw both in recitation and in class, that we can calculate the 3D density of
k),
state corresponding to a given dis
Homework
6, solution
Nicolas Poilvert
Nicola Marzari
November 2, 2007
Homework is due on Thursday November 1st, 5pm
1
11
Thermodynamics of the free electron gas in
3D
Physics at T=0K
Lets consider a parallepiped of sides Lx , Ly and Lz , with free electro
Homework
Nicolas Poilvert
5
Nicola Marzari
October 15, 2007
Homework is due on Wednesday October 17th, 5pm
1
Density of states
We saw both in recitation and in class, that we can calculate the 3D density of
k),
state corresponding to a given dispersion fo
Quantum Mechanics exercise sheet 2
Nicolas Poilvert
September 19 2007
In order to nd the quantum mechanical expression for a physical observable
that has a classical analog, we use the anonical quantization rules. Those
rules state that if a classical obs
3 23 midterm exam Solutions
Nicola Marzari
Nicolas Poilvert
October 31, 2007
1
Question 1 [20 points]
Dene and explain the following concepts, and for each of them explain their
relevance with an example.
a) Commuting operators: o
n
One says that the se
Homework
Nicolas Poilvert
7
Nicola Marzari
November 4, 2007
Homework is due on Thursday November 8st, 5pm
1
Intrinsic semiconductor
Let us consider a 2 band intrinsic semiconductor. From the microscopic point of
view this semiconductor is caracterized by
1) Question 1 [20 points]
Define and explain the following concepts, and for each of them explain their relevance with
an example.
a) Commuting operators
b) Acoustic and optical phonons
c) Time-dependent Schroedinger equation
d) Hartree equations
2) Quest
Homework
Nicolas Poilvert
7
Nicola Marzari
November 1, 2007
Homework is due on Thursday November 8st, 5pm
1
Intrinsic semiconductor
Let us consider a 2 band intrinsic semiconductor. From the microscopic point of
view this semiconductor is caracterized by
Homework
Nicolas Poilvert
6
Nicola Marzari
October 29, 2007
Homework is due on Thursday November 1st, 5pm
1
11
Thermodynamics of the free electron gas in
3D
Physics at T=0K
Lets consider a parallepiped of sides Lx , Ly and Lz , with free electrons inside