5.73 Problem Set 3
Due Friday, Oct. 7
All of these problems concern a particle in a delta function potential:
V (q ) = V0 (q )
where V0 is a constant .Note that the potential is attractive if V0 < 0
and repulsive if V0 > 0 . We want to describe a particle
DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS 02139-4307
Donald R. Sadoway
John F. Elliott Professor of Materials Chemistry
MacVicar Faculty Fellow
3.53 ELECTROCHEMICAL PROCESSING OF MATERIA
DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS 02139-4307
Donald R. Sadoway
John F. Elliott Professor of Materials Chemistry
MacVicar Faculty Fellow
3.53 ELECTROCHEMICAL PROCESSING OF MATERIA
5.73 Problem Set 7
Due: Friday, Dec. 9 2004
1. Consider a diatomic molecule with two electronic states, 1 and
2 and a bond length R. The Hamiltonian for this system in
the diabatic basis is given by:
2
H = 1 1 R + V11 R 1 + 1 V12 ( R ) 2
2
(
+ 2 V21
( )
(
8.333: Statistical Mechanics I
Fall 2007
Test 1
Review Problems
The rst in-class test will take place on Wednesday 9/26/07 from
2:30 to 4:00 pm. There will be a recitation with test review on Friday 9/21/07.
The test is closed book, but if you wish you ma
5.73 Problem Set 1
Due Friday, Sept. 23
1. In class, we talked about linear polarization states. Photons
can also exist in either of two possible circular polarization
states (left and right) that can be written in terms of the
familiar linear polarizatio
8.333: Statistical Mechanics I
Fall 2007
Test 1
Review Problems
The rst in-class test will take place on Wednesday 9/26/07 from
2:30 to 4:00 pm. There will be a recitation with test review on Friday 9/21/07.
The test is closed book, but if you wish you ma
1. Consider a diatomic molecule with two electronic states, 1 and
2 and a bond length R. The Hamiltonian for this system in
the diabatic basis is given by:
2
H = 1 1 R + V11 R 1 + 1 V12 ( R ) 2
2
(
+ 2 V21
( )
(R ) 1 + 2 (
1
2
2
R
( )
+ V22 R 2
where the
5.73 Problem Set 5
1. Consider a system that evolves under the Hamiltonian
H = J z .
Compute the average values J x (t ) , J y (t ) and J z (t ) given
fixed initial values for each average. What is the vector
J = J x (t ) i + J y (t ) j + J z (t ) k doi