Problem 10.18
_ (I L 2_ 2 _
E 41r60(a.-u)3[(c v)u+ax(uxa)]. Herev I (4 1
vi, a = ai, and, for points to the right)? = 5:. So u = LLLFJ
(cv)i, uxa=0,and4-u=a(cv). J:
_ q a 2_ 2 _ ,_ q i(c+v)(cv)2,_ q i c+v -_
E 41T043(C'U)3(c v)(c v)x_41reo2 (cv)3
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Problem 12.6
light signal leaves a at time 11; arrives at earth at time ta = t; + da/c,
light signal leaves b at time t; arrives at earth at time t1, = t, + db/c.
_ _ I
+ (db da) = At' + ( vAt c080)
,-,At=tbta=tg~t; C c
= At [1 Ecos] .
(Here da is the dis
DIFFERENTIAL OPERATORS IN
CURVILINEAR COORDINATES5
Cylindrical Coordinates
Divergence
A=
1
1 A
Az
(rAr ) +
+
r r
r
z
Gradient
(f )r =
f
;
r
(f ) =
1 f
;
r
(f )z =
Curl
( A)r =
A
1 Az
r
z
( A) =
Ar
Az
z
r
( A)z =
1
1 Ar
(rA )
r r
r
Laplacian
1
f =
PHYS W3008: Electricity/Magnetism and Optics (Spring 2013)
Course Webpage: On Courseworks (https:/courseworks.columbia.edu)
Instructor: Professor Brian Metzger (email: bdm2129@columbia.edu)
Office Hours: Monday 12:30-1:30 PM, or by appointment, Pupin 724
QUANTUM MECHANICS LECTURE 39
1. Scattering Review
IN SERT GRAP HIC1
Examining the angle at which a particle scatters naturally leads to an experiment where we measure the
number of particles which pass through d. We then compare the incident flux: Id vs I
Introduction to Quantum Mechanics II
Time-Dependent Perturbation Theory I
Brian Greene
May 3, 2012
1
Introduction
So far we have been able, through various tricks, solve the Schrodinger equation exactly to find the eigenvalues
and eigenfunctions of the sy
Introduction to Quantum Mechanics II
Lecture 1
Brian Greene
January 17, 2012
At the end of last semester, we began analyzing our results from the Schrodinger equation of an electron
within a hydrogen atom and introduced the concept of particle spin. You m
SCATTERING THEORY
ELIZABETH CRITES
APPLIED PHYSICS & APPLIED MATHEMATICS
COLUMBIA UNIVERSITY
ECC2149@COLUMBIA.EDU
1. Introduction:
Much of what we know about nuclear, atomic, and particle physics has come from scattering experiments.
Here are some particu
Introduction to Quantum Mechanics
Lecture 27
Brian Greene
January 31, 2012
1
Rotating Spin States
Suppose you aim a bunch of spin
1
2
particles with random spin orientations at a device which measures the
spin of each particle along the D-axis. This devic
QUANTUM MECHANICS LECTURE 47
1. Measurement Problem
We have already spoken about three possible ways to solve the Measurement problem: MWA, Bohm, and
GRW. MWA and Bohm changes an interpretation, and GRW bites the bullet and suggests the the wave
collapse
QUANTUM MECHANICS III LECTURE 3
1. Analyzing Entanglement
We will be analyzing features of entangled states and analyzing Bohms approach to the entangled states
described in the EPR paper. We described two non-interacting particles as
1 (~x)2 (~y )
where
Introduction to Quantum Mechanics Lecture
37
Brian Greene
March 20, 2012
1
Scattering Theory Set-Up
We have the following set-up: a source of particles is sent out in a columnated beam in the z-direction towards a target (atoms or other things of
which yo
QUANTUM MECHANICS II LECTURE 48: THE LAST LECTURE
1. Feynman Sum Over Histories
CM: Newtons Laws S =
xtR,tf
L(x, x)
dt
xt ,to
where
1 2
mx V (x) = (P E KE)
2
S
= 0, then you have Newtons laws.
If you then ask, which trajectories give you 0,
x
x=xcl
QUANTUM MECHANICS II - LECTURE 4
KATHLEEN TATEM
1. Summary from Last Time
1.1. Notation. Proved Bells Theorem (Bells Inequality)
remember: cfw_Lx , Ly , Lz operators for angular momentum
spin cfw_Sx , Sy , Sz 2x2 matrices acting in the 2-D Hilbert space
Lecture 41: Measurement Problem
Brian Greene
May 1, 2012
All that weve done so far comes from the linearity of the Schrodinger
Equation. That linearity has allowed us to use Fourier transforms and series,
expand eigenstates, diagonalize matrices, and othe
Quantum Mechanics II - Lecture 2
Brian Greene
January 22, 2012
1
Einstein, Podolsky, Rosen
In 1935, Albert Einstein, Boris Podolsky, and Nathan Rosen (EPR) published an interesting and influential
critique against quantum mechanics entitled Can Quantum-Me
QUANTUM MECHANICS III LECTURE 35
1. Selection Rules
Recall from HW 6 and the chapter on Time Dependent Perturbation Theory how we found the matrix
b i. We used Selection Rules to identify which elements were non-zero.
representation of ha |O|
Consider co
QUANTUM MECHANICS II - LECTURE 42
KATHLEEN TATEM
1. Summary from last time:
Measurement Problem:
Linearity of SE = no such thing as wavefunction collapse
[yet this is the heart of making QM predictions]
wave 7 measurement unique outcome
(x) 7 Prob(x0 ) =
QUANTUM MECHANICS II LECTURE 38
In order to compensate for Griffiths treatment of Scattering Theory, we will perform analysis more in
line with Quantum Mechanics this go around. We begin by looking at time dependence and setting up
wave packets in scatter
QUANTUM MECHANICS III LECTURE 36
1. Scattering Theory
The last chapter of the book. However, what Griffiths does is a bit of a cheat. He gets to the right answer,
but between what he does and we do in this class, there are some important pieces of informa
Careers, related to use of the technology
The scientist-geneticist
The results obtained after electrophoresis can tell you everything about the person. You
can trace his ancestry, see some of the mutations, and even look into the future! Therefore,
elect
UNIFORM CIRCULAR MOTION
Purpose: To find relationship between FC , m, r and f
Prediction:
Base on FC = and v=2rf , we predict
If the distance (r) from the stopper to the top of the tube is increasing so the speed will be higher
and the frequency increase