Homework solutions for Classical
Mechanics and Electromagnetism in
Accelerator Physics
The US Particle Accelerator School
January 25 Feb 5, 2016
Day 1
Problem 2.1 Prove that
1
x 0
sin 0 t +
x(t) = x0 cos 0 t +
0
0
Z
t
sin 0 (t t0 )f (t0 )dt0
(1.1)
0
gives
2012
Matthew Schwartz
I-6: The S-matrix and time-ordered products
1 Introduction
As discussed in the previous lecture, scattering experiments have been a fruitful and ecient
way to determine the particles which exist in nature and how they interact. In a
2012
Matthew Schwartz
II-7: Path integrals
1 Introduction
So far, we have studied quantum eld theory using the canonical quantization approach, which
is based on creation and annihilation operators. There is a completely dierent way to do
quantum eld theo
PHYS 203 - Classical Mechanics
Princeton University - Fall 2006
Prof. Michael Romalis
Lectures
Homework Session (optional)
Office Hours:
TA: Marcus K Benna
TA office hours:
Website:
romalis@princeton.edu, Office: Jadwin 230, Phone 8-5586
Tuesday, Thursday
San Jos State University
Department of Physics and Astronomy
Physics 205, Fall, 2016
Course and Contact Information
Instructor:
Patrick Hamill
Office Location:
Sci 240
Telephone:
(408) 924-5241
Email:
Patrick.Hamill@sjsu.edu
Office Hours:
Prerequisites
Cl
PHYSICS 343 Dynamics
Fall 2011
Instructor:
Prof. Ashley Carter
Contact:
118 Merrill Science Center
413-542-2593 (office) or 303-818-8536 (cell/text)
acarter@amherst.edu
Office Hrs:
Prof. Carter - TTh 11:30 12:00 pm, MWF 11:00 12:00 pm
These are official o
Human Biology
Douglas Wilkin, Ph.D.
Jean Brainard, Ph.D.
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Teaching Biological Physics
Why dont students see this and study
more physics?
Perhaps it is because when students read course catalogs, they often
get no hint of the great ferment going
on in our laboratories. Many physics
Raymond E. Goldstein, Philip C.
REDISCOVERING
BIOLOGY
Overview and Credits
Introduction to Project
Goal and intended audience
Rediscovering Biology was designed for high school biology teachers
who have substantial knowledge of basic biology but who want to
learn about important new dis
Physics 106B: Classical Mechanics
Homework 2: Canonical Transformations and the Hamilton Jacobi
Equation
DUE: Thursday, January 23 2003
Remember: Late homework will be granted 50% credit up to one week late. After this, there is
no credit. Extensions requ
Biological Physics
Energy, Information, Life
Philip Nelson
University of Pennsylvania
with the assistance of Marko Radosavljevic and Sarina Bromberg
Appearing July 2003 from W. H. Freeman Co.
Contents at:
http:/www.physics.upenn.edu/~biophys/frontmatter.p
2012
Matthew Schwartz
I-1: Microscopic Theory of Radiation
1 Blackbody Radiation
Quantum mechanics began on October 19, 1900 with Max Plancks explanation of the blackbody radiation spectrum. Actually, although Plancks result helped lead to the development
Matthew Schwartz
2012
I-2: Lorentz Invariance and Second Quantization
1 Introduction
Last time we saw that if we treat each mode of the photon as a separate particle, and give it
multiple excitations like a harmonic oscillator, we can derive Einsteins rel
2012
Matthew Schwartz
II-6: Quantum Electrodynamics
1 Introduction
Now we are ready to do calculations in QED. We have found that the Lagrangian for QED is
1 2
L = F + i D m
4
(1)
with D = + ieA . We have also introduced quantized Dirac elds
d3 p
(2)3
s
2012
Matthew Schwartz
III-1: The Casimir Eect
1 Introduction
Now we come to the real heart of quantum eld theory: loops. Loops generically are innite.
For example, the vacuum polarization diagram in scalar QED is
kp
p
p
= (ie)2
d4k
2k p 2k p
4 (p + k)2 m
Matthew Schwartz
2012
II-3: Spinors
1 Introduction
1
The structure of the periodic table is due largely to the electron having spin 2 . In non-rela1
1
tivistic quantum mechanics you learned that the spin + 2 and spin 2 states of the electron projected alo
2012
Matthew Schwartz
II-4: Spinor solutions and CPT
1 Introduction
In the previous lecture, we characterized the irreducible representations of the Lorentz group
O(1,3). We found that in addition to the obvious tensor representations , A , h etc., there
Matthew Schwartz
2012
II-1: Spin 1 and Gauge Invariance
1 Introduction
Up until now, we have dealt with general features of quantum eld theories. For example, we
have seen how to calculate scattering amplitudes starting from a general Lagrangian. Now we
w
Matthew Schwartz
2012
II-2: Scalar QED
1 Introduction
Now that we have Feynman rules and we know how to quantize the photon, we are very close to
quantum electrodynamics. All we need is the electron, which is a spinor. Before we get into
spinors, however,
2012
Matthew Schwartz
I-7: Feynman Rules
1 Introduction
In the previous lecture we saw that scattering calculations are naturally expressed in terms of
time-ordered products of elds. The S-matrix has the form
f |S |i |T cfw_(x1) (xn)|
(1)
where | is the g
2012
Matthew Schwartz
I-5: Cross Sections and Decay Rates
1 Introduction
The twentieth century witnessed the invention and development of collider physics as an ecient
way to determine which particles exist in nature, their properties, and how they intera
2012
Matthew Schwartz
I-4: Old Fashioned Perturbation Theory
1 Perturbative Quantum Field Theory
The slickest way to perform a perturbation expansion in quantum eld theory is with Feynman
diagrams. These diagrams will be the main tool well use in this cou
2012
Matthew Schwartz
I-3: Classical Field Theory
1 Introduction
We have now seen how quantum eld theory (QFT) is just quantum mechanics with an innite
number of oscillators. We saw that QFT can do some remarkable things, such as explain spontaneous emiss
Matthew Schwartz
2012
II-5: Spin and Statistics
1 Introduction
One of the most profound consequences of merging special relativity with quantum mechanics is
the spin-statistics theorem: states with identical particles of integer spin are symmetric under
t