Quantum Mechanics - exercice sheet 1 solution
Nicolas Poilvert
September 12 2007
By de nition, the De roglie formula is = h , where h is the Planck constant
p
and p is the momentums magnitude. We also know from classical mechanics
that the momentum is rel
MIT 3.320/SMA 5107 Atomistic Modeling of Materials Spring 2005
3.320 Atomistic Modeling of Materials Spring 2005
Problem set 2: First-principles energy methods
Due date 3/22/2005
In the empirical energy lab, we looked at problem-specific convergence issue
Homework
Nicolas Poilvert
3
Nicola Marzari
September 27, 2007
Homework is due on Wednesday October 3rd, 5pm
1
The Scanning Tunneling microscope
The purpose of this exercise is to show how from physical intuition we can
create a physical model for a system
Homework
Nicolas Poilvert
12
Nicola Marzari
December 6, 2007
Numerical answers with no derivation or justi cation will not be credited.
1
Average lifetime of excited carriers.
Consider Figure 5.8 p. 102 of your book Optical Properties of Solids by Mark
Fo
MIT 3.320 Atomistic Modeling of Materials Spring 2005
1
3.320 Atomistic Modeling of Materials Spring 2005
Problem set 3: First-principles energy methods II
Due date: 4/05/2005
In this problem set, we will perform additional first-principles calculations.
Homework
Nicolas Poilvert
4
Nicola Marzari
October 2, 2007
Homework is due on Wednesday October 10th, 5pm
Nodal surfaces in the hydrogen atom
Draw the radial component of the 3s, 3p, and 3d orbitals for the hydrogen atom.
For each of these orbitals, draw
MIT 3.320/SMA 5107 Atomistic Modeling of Materials Spring 2005
3.320 Atomistic Modeling of Materials Spring 2005
Solution set 2: First-principles energy methods
Problem 1 (10 points): Convergence of absolute energies with respect to cutoff energies.
A. Us
Homework
4, solution
Nicolas Poilvert
Nicola Marzari
October 12, 2007
Homework is due on Wednesday October 10th, 5pm
Nodal surfaces in the hydrogen atom
Draw the radial component of the 3s, 3p, and 3d orbitals for the hydrogen atom.
For each of these orbi
MIT 3.320/SMA 5107 Atomistic Modeling of Materials Spring 2005
3.320 Atomistic Modeling of Materials Spring 2005
Problem set 4: Molecular Dynamics
Solution Set
Due date: 4/21/2005
In this problem set, we will examine some of the common features of molecul
Homework
Nicolas Poilvert
3
Nicola Marzari
September 29, 2007
Homework is due on Wednesday October 3rd, 5pm
1
The Scanning Tunneling microscope
The purpose of this exercise is to show how from physical intuition we can
create a physical model for a system
Homework
12 - Solutions
Nicolas Poilvert
Nicola Marzari
December 14, 2007
1
Average lifetime of excited carriers.
a) As time goes by, electrons excited in the conduction band and holes excited
in the valence band relax to lower energy states, causing the
MIT 3.320 Atomistic Modeling of Materials Spring 2005
1
3.320 Atomistic Modeling of Materials Spring 2005
Solution set 3: First-principles energy methods II
Problem 1 (50 pts): Cobalt in HCP and FCC structures.
k -point mesh :
Fig. 1
(a)
(b)
(c)
The dashe
Quantum Mechanics exercice sheet 1
Nicolas Poilvert
September 12 2007
In a monoatomic gas, one measure of the average speed of a gas particle is
q
1/2
the root mean square speed dened as follow: vrms = v 2
= 3km T ,
where kB is the Boltzmann constant, T t
MIT 3.320/SMA 5107 Atomistic Modeling of Materials Spring 2005
3.320 Atomistic Modeling of Materials Spring 2005
Problem set 4: Molecular Dynamics
Due date: 4/21/05
In this problem set, we will examine some of the common features of molecular
dynamics cal