SI Units, Identities and Constants
length: m
mass: kg
time: s
velocity : m/s
acceleration: m/s2
Force: Newton = kgm/s2
2 2
Energy: Joule = kgm /s
Power: Watt = J/s
Charge: C = As
E Field: V/m = N/C
B Field: T = kg/As2
Resistance: Ohm = V/A
12
Inductance:
Physics 2D Quiz #3
Department of Physics, UCSD
Summer Session II - 2010
Prof. Pathria
20 August 2010
Some Useful Data
Speed of light:
c = 2.998 108 m/s
Plancks constant:
h = 6.626 1034 J s
Coulomb constant:
k = 8.99 109 N m2 /C 2
Rydberg constant:
R = 1.0
Physics 2D Quiz #1
Department of Physics, UCSD
Summer Session II - 2010
Prof. Pathria
6 August 2010
Some Useful Data
Speed of light, c = 3 108 m/s.
Lorentz Transformations:
t = (t vx )
c2
t = (t + vx )
c2
x = (x vt)
x = (x + vt )
1
=
2
1 v2
c
Relative Vel
Physics 2D Quiz #4
Department of Physics, UCSD
Summer Session II - 2010
Prof. Pathria
27 August 2010
Some Useful Data
Speed of light:
c = 2.998 108 m/s
Plancks constant:
h = 6.626 1034 J s
Rest mass of an electron:
me = 9.109 1031 kg = 0.511M eV /c2
Rest
Physics 2D Quiz #2
Department of Physics, UCSD
Summer Session II - 2010
Prof. Pathria
13 August 2010
Some Useful Data
Speed of light:
c = 3 108 m/s
c = f
Plancks constant:
h = 6.626 1034 J s
Atomic mass unit (amu):
1amu = 1.66054 1027 kg = 931.5M eV /c2
R
Physics 2D - SS2 2012
Midterm #2
Tuesday, August 28th 3:30pm to 4:50pm
[Note: this is a closed-book exam. No additional notes or calculator are
allowed. The total score of this exam is 80 points. Points assigned to each
problems is thus a guide to how man
Physics 2D - SS2 2012
Midterm #1
Tuesday, August 14th 3:30pm to 4:50pm
[Note: this is a closed-book exam. No additional notes or calculator are
allowed. The total score of this exam is 80 points. Points assigned to each
problems is thus a guide to how man
Physics 2D - SS2 2012
Final Exam
Saturday, September 8th 3:00pm to 5:59pm
[Note: this is a closed-book exam. No additional notes or calculator are
allowed. The total score of this exam is 160 points.]
relativistic energy-momentum relation: E 2 = p2 c2 + m
Homework Set 2
The homework problems have been broken up according to which lecture they are associated with. Feel
free to do them at any time or in any order though. The earlier you start the homework the better. You
probably dont want to wait until the
Homework Set 1
The homework problems have been broken up according to which lecture they are associated with. Feel
free to do them at any time or in any order though. The earlier you start the homework the better. You
probably dont want to wait until the
Errata
(5.19) The work is correct, but the nal answer is o by a factor of 2. The answer
should 45.5 fm not 91 fm.
(6.5) In part A, the potential energy should contain 2x2 /L2 3 in parenthesis instead
of 2x2 2 6. In part B, the potential energy is now zero
Homework Set 1 Solutions
Lecture 1 Problem:
Assume that visible light of wavelength 400 nm was used in a Michelson-Morley experiment, and the
apparatus is capable of measuring differences in paths of two beams as small as that wavelength.
Assuming L = 50
Lecture 30
Review!
Announcements
Final Friday @ 11:30 York 2722
One Page Cheat Sheet! (front and
back)
bring blue book, calculator, pencil
Evenly cover all chapters
Finals Week Ofce Hours:
Bor-Yuan Tuesday 2-3 MH tutorial center
Me: Thurs 1-4pm Es
Review Part 1!
Chapters 1-4
Announcements
Final is June 15, Friday at 11:30 am
The location will be in York 2722
You are allowed a full page (front back) for a
cheat sheet.
Doodle Survey (posted online)
When would you like to have ofce hours during
n
Lecture 28
The Hydrogen Atom
Research Experience as an
Undergraduate
Students who do undergraduate research are more likely to go on to
graduate school, and on average become productive researchers in graduate
school faster. This is most true when undergr
Lecture 25
The Hydrogen Atom! For real!
Last Time
Math overload! (Quick Review?)
3D 3D in spherical coordinates!
r is the radius
is the
inclination
is the azimuth
Time Independent
Schrdinger
(r,t) = (r,)(t)
(r,) = R(r)()()
Last Time
Using the Coulom
Lecture 24
3D-QM
Last Time
Extended our 1-D model to 3-D
x
(r, t ) = (r ) ( t ) = (r )e it
Schrodingers eq:
Time independent
Schrodinger:
Particle in a 3D box
Particle in a 3D box
Solutions will be of the form:
~Asinkx+Bcoskx
Applying boundary
conditi
Lecture 23
Step Function, 3-D!
Last Time
I = Ae ikx + Be ikx
Quantum Tunneling
III = Fe ikx
The Step Potential
I
II
A free particle with E<U incident upon the potential step
Region I (U=0) Free particle wavefunction moving to
the right, with reected
Lecture 22
Quantum Tunneling
Last Time
Expectation Values:
Position:
(Average position)
< x >=
x ( x, t)
2
dx
Momentum:
(Average momentum) < p >=
using the momentum operator:
[ p] =
i x
* i x dx
sandwiching the operator in
between the square
Lecture 21
Expectation Values, Operators,
Uncertainty
Last Time
Quantum Oscillator
When a particle is acted on by a spring-like force where
F=-kx representative of a stable equilibrium
U=1/2Kx2 and =(K/m)
U(x)=(1/2)m2x2
TISE becomes:
E=(1/2)
Last
Lecture 20
The Quantum Oscillator and
Expectation Values
Quiz 3 results posted!
average = 8.7
100
90
80
70
60
50
Series1
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Announcements: No class Friday Sun God!
Quiz 4 is not till June 1st, covering chapter 6 and 7
Use t
Lecture 19
QM in 1-D: Finite Square Well,
Quantum Oscillator,
Expectation Values
Last Time
Particle in a box (Innite Well Problem)
(x)=0
=Asinkx+Bcoskx
(x)=0
Finding a Wavefunction
Guidelines:
1. Determine the form of the potential(s) in your
system
2.
Lecture 18
QM in 1-D: Particle in a box &
Finite Square Well
From Last Time
Can pick up quizzes at Discussion Section and
Problem Session if you did not get it last time.
Wave function, (x,t)
All possible information about a particle is contained in it
Lecture 17
QM in 1-D
Quiz 2 Results!
Average = 6.59
25
20
15
Series1
10
5
0
1
2
3
4
5
6
7
8
9
10
Last Time
Heisenberg Uncertainty Principle:
px x /2
E t /2
The precision with which we can know the
energy of some system is limited by the
time available
Lecture 16
Matter Waves, Heisenberg
Uncertainty Principle
Announcements
Quiz #3 in one week!
Covers chapters 4 and 5
Class Cancelled May 14th
Last Time
Goal: Describe a particle as a
pulse or a wave group
Review of traveling waves
Review of wave add
Lecture 15
More Matter Waves!
Last Time
De Broglies PhD thesis:
Matter has wave-like properties
Matter has a pilot-wave that steers it through
space and time
Electron-Wave Experiments
The Davisson-Germer Experiment 1927
Electron-Wave Experiments
Doub