Physics 70007, Fall 2009
Solutions to HW #4
November 2009
1. (Sakurai 2.11)
Consider a particle subject to a one-dimensional simple harmonic oscillator potential. Suppose at
t = 0 the state vector is given by
exp
ipa
~
|0i
where p is the momentum operator
Physics 70007, Fall 2009
Solutions to Homework #3
October 30, 2009
1. (Sakurai 1.28)
(a) Let
x
and
px
be the coordinate and linear momentum in one dimension. Evaluate the classical
Poisson bracket
[x, F (px )]classical
The classical Poisson bracket is den
Physis 70007, Fall 2009
Solutions to HW #5
Deember 2, 2009
1. Consider the ase of a partile with mass m in an innite potential well dened by a potential V (x) = 0
for 0 x L and V (x) = otherwise.
(a) Find the eigenfuntions n (x) and the energy spetrum En
1(35) The Unknown Central Force
y
An object of mass m is acted on by an unknown central force which causes it to travel
in a circular path of radius R about the force
center. As shown in the figure to the right,
the object is moving with constant angular
1(25) Short Answer Questions
a(5) Using m, l and t as the symbols for the dimension of mass, length and
time, what are the dimensions of force and momentum?
The units of force are Newtons, or kg m/s2 . For momentum, we have mass
times velocity, or kg m/s.
Physics 70007, Fall 2009
Answers to HW set #1
September 27, 2009
1. Convince yourself that x and p are Hermitian operators, and show that the phonon creation
operator a is the Hermitian adjoint of the phonon destruction operator a.
Since position and mome
1(40) Gravitational Systems
Two heavy spherical (radius 0.05R) objects are located at fixed positions along
2M
m
2M
0
R
an axis in space. The first mass is centered at r = 0 and has a mass of 2M .
The second mass is centered at r = R and has a mass of 2M
1(50) Quantum Systems
A quantum object is known to have five energy levels. In order to learn about the
system, you shine light on a cold collection of many of these objects. In measuring the
light coming through the system, you observe that the following
1(50) Mr Conehat is developing a stunt for the circus using a spring-like device that he has
developed. He calls it a sproing, and notes that like a spring, the stored potential energy
depends on the compression or stretch of the sproing. If he defines th
1(50) The Gas Cloud
A small satellite of mass m has been placed in a circular orbit around the center
of a large, spherical, uniform density, c , gas cloud of radius R. The satellites
orbit, with radius r, is actually inside of the cloud, but the clouds d
Matter & Interactions I: 33131
Fall 2010
Exam, 22 October, 2010
Name (print) Solution Key
Last,
First
Section:
Name (sign)
This exam is 8 pages long. If you are missing a page, please contact the invigilator
(proctor). There are 100 points possible in thi
1(35) Two masses, m1 and m2 undergo a collision. As seen in the lab frame, m1 is
initially moving with velocity ~v1 = v1 x and m2 is at rest. This is shown in the
picture below. We will consider the system of the two masses both before, and
after the coll
Exam #1
Chapters 1-5
Tuesday February 23, 2016
Practice Exam and Equation Sheet
A nucleus A has a half-life T and nucleus B has a half-life 2T. Initially the
number of nuclei of type A equals the number of nuclei of type B. After a
certain time, 10% of th
PHYSICS III
Multiple choice: 11 pts each
1. A newly created particle is moving through the laboratory at a speed of 0.45 c. It is observed
to live for a time of 0.231 s before decaying. What would be the lifetime of this particle
according to someone who
Department of Physics
Physics III: Modern Physics Course Information
Physics 20330-01
Spring 2016
Instructor:
Ani Aprahamian
Freimann Professor of Physics
183 Nieuwland Science Hall
Tel: 574 631-8120
Email: aapraham@nd.edu
Class Meeting times:
Tuesday/Thu
Physics III: Homework Procedures and Evaluation
Spring 2016
The real learning in this course takes place while doing the homework. The
homework is worth 30% of the grade for the course. In this course, we are going to
handle the homework somewhat differen
Modern Physics Examination 1
Equation Sheet
Physics 20330-01
Chapter 1:
Chapter 2:
Chapter 3:
Energy of a photon
E=hf=hc/
Maximum kinetic energy of photoelectrons
I=T4
Kmax= eVs= hf-
Wiens displacement law
maxT=2.8978x10-3 m.K
Plancks blackbody distribut
ExperimentalDesign
The process of doing science requires explicit knowledge
(formally written definitions) and tacit knowledge (formal
expectationsandnorms).Experimentaldesignnavigatesboth.
ExperimentalDesignPathways
PhysicsResearchQuestion/Hypothesis/Co
Error in Measurements and Analysis
In Experimental Designs
Abigail Mechtenberg
University of Notre Dame
Assistant Teaching Professor
Physics Department, College of Science
Experimental Design Purpose
(1) Research Ques&on, OR
(2) Hypothesis (predi
Error Propagation
Uncertainty
Uncertainty reflects the
knowledge that a measured
value is related to the mean.
Probable error is the range from
the mean with a 50% certainty.
For a normal distribution:
0.675
Coefficient of Variation
The coefficient of va