Homework 1
AS.171.303: Quantum Mechanics I
Due: Tuesday, September 24
1. (a) Dimensional analysis is a very useful skill for all aspects of physics. For example,
lets determine one of the fundamental length scales associated with the electron,
often calle

MIEF Quantitative Methods I (Econometrics)
Class 3 Matrices
Project the Comparison of the Algebra of Matrices to the Algebra of Real Numbers
Start by reviewing what we mean by the algebra of real numbers based on the seven axioms and some
definitions.
Pro

Final Exam
AS.171.303: Quantum Mechanics I
Saturday, December 14, 2013
This is a closed book exam. Please be sure to show ALL essential steps of your work.
The exam is scored out of 200 points. You will have 3 hours to complete this exam.
1. (30 pts) A Ha

Homework 10
AS.171.303: Quantum Mechanics I
Due: Monday, December 9
1. A particle of mass m is in a one-dimensional harmonic oscillator with angular frequency
.
(a) If the particle is initially in the Hamiltonian eigenstate |n , and the action of the
rais

Homework 9
AS.171.303: Quantum Mechanics I
Due: Tuesday, November 26
1. A particle of mass m is in the ground state of an innite square well of width a.
Suddenly the well expands to twice its size, with the right wall moving from x = a
to x = 2a, while th

Homework 8
AS.171.303: Quantum Mechanics I
Due: Tuesday, November 19
1. A particle of mass m is in the potential energy well
0 0<x<L
elsewhere
V (x) =
Solve the energy eigenvalue equation
H| = E|
in position-space to show that the energy eigenvalues are

Homework 7
AS.171.303: Quantum Mechanics I
Due: Friday, November 8
1. A particle is in the state | , such that the one-dimensional position-space wavefunction
is
(x) x| =
1
2
2
e(xc) /2a
2 )1/4
(a
(a) What is the probability of measuring the particle to b

Homework 5
AS.171.303: Quantum Mechanics I
Due: Tuesday, October 29
1. Show that if the Hamiltonian depends on time and [H(t1 ), H(t2 )] = 0 for all times
t1 , t2 , the time-evolution operator is given by
t
i
U (t) = exp
dt H(t )
0
2. An s = 1 particle i

Homework 4
AS.171.303: Quantum Mechanics I
Due: Tuesday, October 15
3
1. A beam of particles with spin angular momentum s = 2 enters a Stern-Gerlach device,
3
which only allows particles measured to be in the |s = 2 , mx = + 1 state to exit. The
2
spin z-

Homework 6
AS.171.303: Quantum Mechanics I
Due: Tuesday, November 5
1. An electron with spin s =
1
2
is in a system such that it has orbital angular momentum
l = 1. The total angular momentum of this electron is therefore J L + S. We want
to nd all of t

Homework 3
AS.171.303: Quantum Mechanics I
Due: Tuesday, October 9
1. A particle with angular momentum quantum number j = 1 can be described using a
3 3 matrix representation. The corresponding representations of the three generators
Jx , Jy , and Jz in

Homework 2
AS.171.303: Quantum Mechanics I
Due: Tuesday, October 1
1. As discussed in class, we can simplify calculations by using a 22 matrix representation
for spin, since the only two degrees of freedom are spin-up and spin-down. If we work
0
1
.
and |

MIEF Quantitative Methods I (Econometrics)
Class 1. Two Variable Regression - Least Squares Estimation and Functional Forms
1. Project Syllabus. Overview of econometrics and the course. Grading. Function fitting. Text
book. Problem sets. Note that the stu